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Select all that apply.\n\n\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"checkbox\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 1 \" value=\"A\"\u003e\u003cb\u003e A. \u003c/b\u003e Division on \\(\\mathbb{Q}\\) \u003cbr\u003e\u003c/label\u003e\n\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"checkbox\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 2 \" value=\"B\"\u003e\u003cb\u003e B. \u003c/b\u003e Subtraction on \\(\\mathbb{Q}\\) \u003cbr\u003e\u003c/label\u003e\n\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"checkbox\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 3 \" value=\"C\"\u003e\u003cb\u003e C. \u003c/b\u003e Function composition on \\(D_4\\)\u003cbr\u003e\u003c/label\u003e\n\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"checkbox\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 4 \" value=\"D\"\u003e\u003cb\u003e D. \u003c/b\u003e Subtraction on \\(\\mathbb{N}\\) \u003cbr\u003e\u003c/label\u003e\n\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"checkbox\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 5 \" value=\"E\"\u003e\u003cb\u003e E. \u003c/b\u003e Multiplication on \\(\\mathbb{Z}\\)\u003cbr\u003e\u003c/label\u003e\n\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"checkbox\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 6 \" value=\"F\"\u003e\u003cb\u003e F. \u003c/b\u003e Addition on \\(\\mathbb{R}\\)\u003cbr\u003e\u003c/label\u003e\n\u003cbr\u003e\u003clabel\u003e\u003cinput type=\"checkbox\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 option 7 \" value=\"G\"\u003e\u003cb\u003e G. \u003c/b\u003e None of the above\u003c/label\u003e\u003cbr\u003e\u003c/p\u003e","header_text":{"css":[],"js":[],"inlinejs":[]}}],"instructional":false,"sketchable":true,"print_num_spacing_lines":3,"print_page_break":false,"readonly":{"created_at":"2022-01-16T15:20:59.908Z","updated_at":"2022-01-16T15:20:59.908Z","version":160,"user_id":"5d376468cec634733edb3e9f","name":"Algorithmic (WebWorK)","skill_ids":[],"current_digest":"mTl/5s+tP/C06RPnLUqkKXMs7eG8GW0l5Iw2EuB9Gxg=","tags":"binary","points":1.0,"type":"webwork","multipart":false,"shallow":true,"static":true,"sources":[],"owned":false,"url":"/problems/61e437dbcc19890004d44a59","searchable_text":"mc print q mc print a","abilities":["read"]}},"readonly":{"shallow":true}}},"readonly":{"level_range":"13","created_at":"2022-03-24T14:22:13.511Z","updated_at":"2024-09-01T18:42:22.154Z","tags":"","author_ids":[],"licensed":true,"thumbnail":"https://d2b8iahp55539n.cloudfront.net/assets/course-placeholder-3870b2677a589ef8debd801ef338e9403ad9236f1e4562739f9efbd8e456503c.webp","free":false,"user_price":29.0,"term_price":29.0,"displayed_price":29.0,"levels":"13"}},{"id":"5c735527c6e851001a2555ad","name":"APEX Calculus (Hartman)","summary":"Edfinity is supported by the National Science Foundation","description":"\u003cp dir=\"ltr\"\u003eThis is an online homework companion to \u003cstrong\u003eAPEX Calculus\u003c/strong\u003e. It comprises hundreds of algorithmic problems carefully organized into problem sets mapped to textbook sections. Use this course as-is, or customize at any level. You can mix-and-match problems from other catalog courses, add problems from the Edfinity problem repository, or write your own.\u003c/p\u003e\u003cp dir=\"ltr\"\u003e\u003cstrong\u003eHow to use this course\u003c/strong\u003e\u003c/p\u003e\u003col\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eHomework\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Assign high quality problems with hints and personalized feedback to develop problem-solving skills.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eTesting\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Create summative secure online quizzes and tests in minutes.\u0026nbsp;\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eSupplementary resources:\u003c/strong\u003e Embed videos, class notes, and applets alongside assignments.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eIntervention:\u003c/strong\u003e Use rich analytics to identify and monitor at-risk students for timely intervention.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eAnalytics:\u003c/strong\u003e Drill down into student performance and identify problematic or difficult topics.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eFlipped classroom:\u003c/strong\u003e Assign pre-class assignments. Save precious class time for discussions.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eEmporium classes:\u003c/strong\u003e Use Edfinity for individual/group work for large enrollment sections in labs.\u003c/li\u003e\u003c/ol\u003e","description_more":"\u003cp\u003eThis course was curated by Gregory Hartman (Virginia Military Institute), Shaun Ault (Valdosta State University), Tien Chih (MSU Billings), Alex Jordan (Portland Community College), and the Edfinity team.\u0026nbsp;\u003c/p\u003e","price":29.0,"sort_order":0,"active":true,"individual_license":false,"section_id":"5c6c57d0d635b100047a271a","permissive_license":false,"type":"course","section_license":true,"taxable":false,"purchasable":true,"related_product_ids":["5c533d7d78811e0e5904234d","5c58eabf4a8e21002b802892","5c6c7c0e7758b300165b7b6e","5c6cb0717758b325775b77fe","5f16ff9e4a1e8d1366b8f2b1"],"audience":"educator_audience","site_ids":["55843bd46435650003000000"],"show_toc":true,"author_roles":[],"author_role_title":"Contributors (Alphabetical)","tags_array":["calculus","oer"],"hidden_tags":["oer","adaptive"],"term_pricing":true,"highlights":"\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-subscript fa-fw mr-2\"\u003e\u003c/i\u003e \u003cstrong\u003eInteractive, algorithmic problems\u003cbr\u003e\u003c/strong\u003eAlgebraic, graphing, open response; randomized variants, hints, and tips\u003c/div\u003e\n\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-hand-holding-heart fa-fw mr-2\"\u003e\u003c/i\u003e\u003cstrong\u003eAdaptive learning and personalization\u003cbr\u003e\u003c/strong\u003eEach student receives personalized support\u003cbr\u003eto fill learning gaps.\u003c/div\u003e\n\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-fw fa-code-branch mr-2\"\u003e\u003c/i\u003e\u003cstrong\u003eCorequisite course structures\u003cbr\u003e\u003c/strong\u003eUse pre-built corequisite content,\u003cbr\u003eor create your own.\u003c/div\u003e\n\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-hands-helping fa-fw mr-2\"\u003e\u003c/i\u003e\u003cstrong\u003eLMS integration and accessibility\u003cbr\u003e\u003c/strong\u003eConnect to your LMS in minutes. \u003ca class=\"”underline”\" href=\"http://edfinity.com/vpat\" target=\"_blank\"\u003eVPAT here\u003c/a\u003e.\u003c/div\u003e\n\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-plug fa-fw mr-2\"\u003e\u003c/i\u003e\u003cstrong\u003eWeBWorK-compatible\u003cbr\u003e\u003c/strong\u003eImport and author WeBWorK problems.\u003c/div\u003e\n","preview_assignment":{"id":"5c6c57d0d635b100047a271d","name":"1.1 An Introduction to Limits","product":{"id":"5c735527c6e851001a2555ad","name":"APEX Calculus (Hartman)"},"master_set":{"id":"66e8bc98cfa660000293891f","problems":{"id":"64b053ded9aed500023f13a7","proof":false,"graphical_geometric":false,"tags_array":[],"skill_ids":["5a139c2bc0421000041a00a2","5a141cc2ac370c0004c7588d","5a139c2bc0421000041a00a2","5a141cc2ac370c0004c7588d","5a1f39a1dbc33f00041a1914","5a141cc2ac370c0004c7588d","5a1f39a1dbc33f00041a1914"],"contest_event_ids":[],"header":"","solution":"","part_attributes":[{"id":"5a139c2dc0421000041a00d6","part_id":"5a139c2dc0421000041a00d5","description":null,"points":4.0,"automatic_manual_credit":true,"format":"ww","pg":"#Problem APEX 1.1.19\n\n## Updated by the Edfinity Team in 2022\n\nDOCUMENT();\n\n# Load whatever macros you need for the problem\nloadMacros(\n  \"PGstandard.pl\",\n  \"PGchoicemacros.pl\",\n  \"PGcourse.pl\",\n  \"MathObjects.pl\",\n  \"PGML.pl\",\n);\n\n## DBsubject(Calculus - single variable)\n## DBchapter(Limits and continuity)\n## DBsection(Estimating limits numerically)\n## Institution(Valdosta State University)\n## Author(S. V. Ault)\n## MLT(newtonquotient)\n## Level(2)\n## TitleText1('APEX Calculus')\n## AuthorText1('Hartman')\n## EditionText1('3.0')\n## Section1('1.1')\n## Problem1('19')\n\n$showPartialCorrectAnswers = 0;\n$solutionexits=1;\n$a=random(0,6);\n$b=random(1,10);\n$c=random(1,10);\n\n$h1=0.1;\n$h01=0.01;\n\n$hx1=-0.1;\n$hx01=-.01;\n\n$ans1 = -$b / ( ($a + $c) * ($a + $h1 + $c) );\n$ans2 = -$b / ( ($a + $c) * ($a + $hx1 + $c) );\n$ans3 = -$b / ( ($a + $c) * ($a + $h01 + $c) );\n$ans4 = -$b / ( ($a + $c) * ($a + $hx01 + $c) );\n\nTEXT(beginproblem());\n\nBEGIN_PGML\n\nA function [`f`] and value [`a`] are given below.  \n\n[``` f(x) = \\frac{[$b]}{x + [$c]}, \\qquad a = [$a] ```]\n\nApproximate the limit of the difference quotient,\n\n[``` \\lim\\limits_{h \\to 0} \\frac{f(a+h) - f(a)}{h}, ```]\n  \nusing [`h = \\pm 0.1, \\pm 0.01`].\n*(Round your answer to within three decimal places if necessary, but \ndo not round until your final computation.)*\n\na.  When [` h = [$h1] `], [` \\dfrac{f(a+h) - f(a)}{h} = `] [__].\n\nb.  When [` h = [$hx1] `], [` \\dfrac{f(a+h) - f(a)}{h} = `] [__].\n\nc.  When [` h = [$h01] `], [` \\dfrac{f(a+h) - f(a)}{h} = `] [__].\n\nd.  When [` h = [$hx01] `], [` \\dfrac{f(a+h) - f(a)}{h} = `] [__].\n\nEND_PGML\n\n\n\nSOLUTION(EV3(\u003c\u003c'END_SOLUTION'));\n\nSubstitute each value of \\(h\\) into the expression\n\\( \\dfrac{f(a+h) - f(a)}{h} \\).\n$BR\n$BCENTER\n\\{begintable(2)\\}\n        \\{row(\" \\(h\\) \", \" \\( \\frac{f(a+h) - f(a)}{h} \\) \", @firstrow)\\}\n        \\{row(\" \\($h1\\) \", \" \\($ans1\\) \" , @secondrow)\\}\n        \\{row(\" \\($hx1\\) \", \" \\($ans2\\) \" , @thirdrow)\\}\n        \\{row(\" \\($h01\\) \", \" \\($ans3\\) \" , @fourthrow)\\}\n        \\{row(\" \\($hx01\\) \", \" \\($ans4\\) \" , @fifthrow)\\}\n        \\{endtable()\\}$BR\n$ECENTER\nEND_SOLUTION\n\n\n#ANS( num_cmp( $ans1 ) );\n#ANS( num_cmp( $ans2 ) );\n#ANS( num_cmp( $ans3 ) );\n#ANS( num_cmp( $ans4 ) );\n\nContext()-\u003eflags-\u003eset(tolerance =\u003e 0.001, tolType =\u003e \"absolute\");\nContext()-\u003e{format}{number} = \"%.12f#\";\nforeach $an ($ans1,$ans2,$ans3,$ans4) {ANS(Compute($an)-\u003ecmp())};\n\nENDDOCUMENT();\n","use_equation_editor":null,"webwork_features":[],"part_attributes":[{"id":"64b052dad9aed500023f12b9","part_id":"5a139c2dc0421000041a00d8","description":null,"points":1.0,"automatic_manual_credit":true,"answer":"-0.00819000819","format":"ws","answer_name":"AnSwEr0001","extra":false,"applet_state":false,"multipart":true,"manually_gradable":false,"answer_text":"\\(-0.00819000819\\)"},{"id":"64b052dad9aed500023f12ba","part_id":"5a139c2dc0421000041a00d9","description":null,"points":1.0,"automatic_manual_credit":true,"answer":"-0.00834028357","format":"ws","answer_name":"AnSwEr0002","extra":false,"applet_state":false,"multipart":true,"manually_gradable":false,"answer_text":"\\(-0.00834028357\\)"},{"id":"64b052dad9aed500023f12bb","part_id":"5a139c2dc0421000041a00da","description":null,"points":1.0,"automatic_manual_credit":true,"answer":"-0.008256956486","format":"ws","answer_name":"AnSwEr0003","extra":false,"applet_state":false,"multipart":true,"manually_gradable":false,"answer_text":"\\(-0.008256956486\\)"},{"id":"64b052dad9aed500023f12bc","part_id":"5a139c2dc0421000041a00db","description":null,"points":1.0,"automatic_manual_credit":true,"answer":"-0.008271982794","format":"ws","answer_name":"AnSwEr0004","extra":false,"applet_state":false,"multipart":true,"manually_gradable":false,"answer_text":"\\(-0.008271982794\\)"}],"interactive_html":"\n\u003cdiv class=\"PGML\"\u003e\nA function \\(f\\) and value \\(a\\) are given below.\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\\[f(x) = \\frac{1}{x + 5}, \\qquad a = 6\\]\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nApproximate the limit of the difference quotient,\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\\[\\lim\\limits_{h \\to 0} \\frac{f(a+h) - f(a)}{h},\\]\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nusing \\(h = \\pm 0.1, \\pm 0.01\\).\n\u003cb\u003e(Round your answer to within three decimal places if necessary, but \ndo not round until your final computation.)\u003c/b\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003col type=\"a\" style=\"margin:0; padding-left:2.25em\"\u003e\n\u003cli\u003eWhen \\(h = 0.1\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cinput type=\"text\" class=\"codeshard\" size=\"2\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0001\" value=\"\"\u003e\n.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhen \\(h = -0.1\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cinput type=\"text\" class=\"codeshard\" size=\"2\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0002\" value=\"\"\u003e\n.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhen \\(h = 0.01\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cinput type=\"text\" class=\"codeshard\" size=\"2\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0003\" value=\"\"\u003e\n.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhen \\(h = -0.01\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cinput type=\"text\" class=\"codeshard\" size=\"2\" name=\"AnSwEr0004\" id=\"AnSwEr0004\" aria-label=\"answer 4 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0004\" value=\"\"\u003e\n.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class=\"solution\"\u003e\n\u003cp\u003e\u003cb\u003eSolution:\u003c/b\u003e \u003cbr\u003e\nSubstitute each value of \\(h\\) into the expression\n\\(\\dfrac{f(a+h) - f(a)}{h}\\).\n\u003cbr\u003e\n\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n\u003ctable border=\"1\" style=\"text-align:center;\"\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(h\\) \u003c/td\u003e\n\u003ctd\u003e \\(\\frac{f(a+h) - f(a)}{h}\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(0.1\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00819000819000819\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(-0.1\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00834028356964137\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(0.01\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00825695648583932\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(-0.01\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00827198279427579\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003c/table\u003e\n\u003cbr\u003e\n\u003c/div\u003e\n\n\u003c/div\u003e","static_html":"\u003cdiv class=\"PGML\"\u003e\nA function \\(f\\) and value \\(a\\) are given below.\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\\[f(x) = \\frac{1}{x + 5}, \\qquad a = 6\\]\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nApproximate the limit of the difference quotient,\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\\[\\lim\\limits_{h \\to 0} \\frac{f(a+h) - f(a)}{h},\\]\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nusing \\(h = \\pm 0.1, \\pm 0.01\\).\n\u003cb\u003e(Round your answer to within three decimal places if necessary, but \ndo not round until your final computation.)\u003c/b\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003col type=\"a\" style=\"margin:0; padding-left:2.25em\"\u003e\n\u003cli\u003eWhen \\(h = 0.1\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cspan class=\"ww-blank\" name=\"AnSwEr0001\"\u003e \u003c/span\u003e\n\n.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhen \\(h = -0.1\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cspan class=\"ww-blank\" name=\"AnSwEr0002\"\u003e \u003c/span\u003e\n\n.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhen \\(h = 0.01\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cspan class=\"ww-blank\" name=\"AnSwEr0003\"\u003e \u003c/span\u003e\n\n.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhen \\(h = -0.01\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cspan class=\"ww-blank\" name=\"AnSwEr0004\"\u003e \u003c/span\u003e\n\n.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class=\"solution\"\u003e\n\u003cp\u003e\u003cb\u003eSolution:\u003c/b\u003e \u003cbr\u003e\nSubstitute each value of \\(h\\) into the expression\n\\(\\dfrac{f(a+h) - f(a)}{h}\\).\n\u003cbr\u003e\n\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n\u003ctable border=\"1\" style=\"text-align:center;\"\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(h\\) \u003c/td\u003e\n\u003ctd\u003e \\(\\frac{f(a+h) - f(a)}{h}\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(0.1\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00819000819000819\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(-0.1\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00834028356964137\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(0.01\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00825695648583932\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(-0.01\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00827198279427579\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003c/table\u003e\n\u003cbr\u003e\n\u003c/div\u003e\n\n\u003c/div\u003e","header_text":{"css":[],"js":[],"inlinejs":[]}}],"instructional":false,"sketchable":true,"print_num_spacing_lines":3,"print_page_break":false,"readonly":{"created_at":"2023-07-13T19:43:26.888Z","updated_at":"2023-07-13T19:43:26.888Z","version":110,"user_id":"58ecdcd48ccf1800120c8ac3","name":"Algorithmic (WebWorK)","skill_ids":["5a139c2bc0421000041a00a2","5a141cc2ac370c0004c7588d","5a139c2bc0421000041a00a2","5a141cc2ac370c0004c7588d","5a1f39a1dbc33f00041a1914","5a141cc2ac370c0004c7588d","5a1f39a1dbc33f00041a1914"],"current_digest":"rIgfyhCfgO2jq1anz0TSGPpixzVHVkrl/byssvi7EPs=","tags":"","points":4.0,"type":"webwork","multipart":true,"shallow":true,"static":true,"sources":[],"owned":false,"url":"/problems/64b053ded9aed500023f13a7","searchable_text":"Substitute each value of h into the expression dfrac f a h f a h BCENTER begintable 2 row h frac f a h f a h firstrow row h1 ans1 secondrow row hx1 ans2 thirdrow row h01 ans3 fourthrow row hx01 ans4 fifthrow endtable ECENTER A function f and value a are given below f x frac b x c qquad a a Approximate the limit of the difference quotient limlimits h to 0 frac f a h f a h using h pm 0 1 pm 0 01 Round your answer to within three decimal places if necessary but do not round until your final computation a When h h1 dfrac f a h f a h b When h hx1 dfrac f a h f a h c When h h01 dfrac f a h f a h d When h hx01 dfrac f a h f a h","abilities":["read"]}},"readonly":{"shallow":true}}},"readonly":{"level_range":"13","created_at":"2019-02-25T02:38:31.563Z","updated_at":"2024-09-16T23:17:46.191Z","tags":"calculus,oer","author_ids":[],"licensed":true,"thumbnail":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c735527c6e851001a2555ad/thumb_apex-calculus.png","free":false,"user_price":29.0,"term_price":29.0,"displayed_price":29.0,"levels":"13"},"image":{"url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c735527c6e851001a2555ad/apex-calculus.png","thumb_url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c735527c6e851001a2555ad/thumb_apex-calculus.png"}},{"id":"5d4b103d93f2cf115b06c974","name":"APEX Precalculus","summary":"Edfinity is supported by the National Science Foundation","description":"\u003cp dir=\"ltr\"\u003eThis is an online homework companion to \u003cstrong\u003eAPEX Precalculus\u003c/strong\u003e. It comprises hundreds of algorithmic problems carefully organized into problem sets mapped to textbook sections. Use this course as-is, or customize at any level. You can mix-and-match problems from other catalog courses, add problems from the Edfinity problem repository, or write your own.\u003c/p\u003e\u003cp dir=\"ltr\"\u003e\u003cstrong\u003eHow to use this course\u003c/strong\u003e\u003c/p\u003e\u003col\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eHomework\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Assign high quality problems with hints and personalized feedback to develop problem-solving skills.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eTesting\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Create summative secure online quizzes and tests in minutes.\u0026nbsp;\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eSupplementary resources:\u003c/strong\u003e Embed videos, class notes, and applets alongside assignments.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eIntervention:\u003c/strong\u003e Use rich analytics to identify and monitor at-risk students for timely intervention.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eAnalytics:\u003c/strong\u003e Drill down into student performance and identify problematic or difficult topics.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eFlipped classroom:\u003c/strong\u003e Assign pre-class assignments. Save precious class time for discussions.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eEmporium classes:\u003c/strong\u003e Use Edfinity for individual/group work for large enrollment sections in labs.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003e\u003ca data-toggle=\"collapse\" href=\"https://edfinity.com/products/5c735527c6e851001a2555ad#collapseMore\"\u003e\u003cbr\u003e\u003c/a\u003e\u003c/p\u003e","description_more":"\u003cp\u003eThis course was curated by Amy Chapman and the Edfinity Team. For details on the authorship of APEX Precalculus, please refer to the APEX Precalculus website.\u003c/p\u003e","price":29.0,"sort_order":0,"active":true,"individual_license":false,"section_id":"5c9a946b084e1976be0a3bb2","permissive_license":false,"type":"course","section_license":true,"taxable":false,"purchasable":true,"related_product_ids":[],"audience":"educator_audience","site_ids":["55843bd46435650003000000"],"show_toc":true,"author_roles":[],"author_role_title":"Authors","tags_array":["precalculus","College_Algebra","oer"],"hidden_tags":["oer"],"term_pricing":true,"highlights":"\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-subscript fa-fw mr-2\"\u003e\u003c/i\u003e \u003cstrong\u003eInteractive, algorithmic problems\u003cbr\u003e\u003c/strong\u003eAlgebraic, graphing, open response; randomized variants, hints, and tips\u003c/div\u003e\n\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-hand-holding-heart fa-fw mr-2\"\u003e\u003c/i\u003e\u003cstrong\u003eAdaptive learning and personalization\u003cbr\u003e\u003c/strong\u003eEach student receives personalized support\u003cbr\u003eto fill learning gaps.\u003c/div\u003e\n\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-fw fa-code-branch mr-2\"\u003e\u003c/i\u003e\u003cstrong\u003eCorequisite course structures\u003cbr\u003e\u003c/strong\u003eUse pre-built corequisite content,\u003cbr\u003eor create your own.\u003c/div\u003e\n\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-hands-helping fa-fw mr-2\"\u003e\u003c/i\u003e\u003cstrong\u003eLMS integration and accessibility\u003cbr\u003e\u003c/strong\u003eConnect to your LMS in minutes. \u003ca class=\"”underline”\" href=\"http://edfinity.com/vpat\" target=\"_blank\"\u003eVPAT here\u003c/a\u003e.\u003c/div\u003e\n\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-plug fa-fw mr-2\"\u003e\u003c/i\u003e\u003cstrong\u003eWeBWorK-compatible\u003cbr\u003e\u003c/strong\u003eImport and author WeBWorK problems.\u003c/div\u003e\n","preview_assignment":{"id":"5c9aacc8084e1976be0a3fcb","name":"1.1 Real Numbers","product":{"id":"5d4b103d93f2cf115b06c974","name":"APEX Precalculus"},"master_set":{"id":"61ddd8199f1cb20003e0285a","problems":{"id":"5e079c75de359200036c0aaf","proof":false,"graphical_geometric":false,"tags_array":[],"skill_ids":["5a1377cdc042100004172ac6","5a141d66ac370c0004c75e23","5a1377cdc042100004172ac6","5a141d66ac370c0004c75e23","5a1f0112dbc33f0004182c44"],"contest_event_ids":[],"header":"","solution":"","part_attributes":[{"id":"5a1377e3c042100004172ca3","part_id":"5a1377e3c042100004172ca2","description":null,"points":1.0,"automatic_manual_credit":true,"format":"ww","pg":"##DESCRIPTION\n##   Evaluation of a simple algebraic expression\n##ENDDESCRIPTION\n\n## hcao tagged and PAID on 12-12-2003\n\n## DBsubject(Algebra)\n## DBchapter(Algebra of real numbers and simplifying expressions)\n## DBsection(Evaluating expressions)\n## Date(6/3/2002)\n## Level(2)\n## TitleText1('College Algebra')\n## AuthorText1('Stewart, Redlin, Watson')\n## EditionText1('3')\n## Section1('1.2')\n## Problem1('50')\n## KEYWORDS('algebra')\nDOCUMENT(); 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is the slope of the line through (0,\n0) and (4,0)?\nIf the slope is undefined, type \u003ci\u003e undefined\u003c/i\u003e.\n\u003cbr\u003e\n\u003cinput type=\"text\" class=\"codeshard\" size=\"30\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 \" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0001\" value=\"\"\u003e\n\n\u003cbr\u003e\n\n\u003c/p\u003e\n\u003cp\u003e\nWhat is the slope of the line through (-5,\n5) and (-5,3)?\nIf the slope is undefined, type \u003ci\u003e undefined\u003c/i\u003e.\n\u003cbr\u003e\n\u003cinput type=\"text\" class=\"codeshard\" size=\"30\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 \" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0002\" value=\"\"\u003e\n\n\u003cbr\u003e\n\nWhat is the slope of the line through (10,\n-10) and (-8,-3)?\nIf the slope is undefined, type \u003ci\u003e undefined\u003c/i\u003e.\n\u003cbr\u003e\n\u003cinput type=\"text\" class=\"codeshard\" size=\"30\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 \" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0003\" value=\"\"\u003e\n\n\u003cbr\u003e\n\n\u003c/p\u003e","static_html":"\u003cp\u003e\nWhat is the slope of the line through (0,\n0) and (4,0)?\nIf the slope is undefined, type \u003ci\u003e undefined\u003c/i\u003e.\n\u003cbr\u003e\n\u003cspan class=\"ww-blank\" name=\"AnSwEr0001\"\u003e \u003c/span\u003e\n\n\n\u003cbr\u003e\n\n\u003c/p\u003e\n\u003cp\u003e\nWhat is the slope of the line through (-5,\n5) and (-5,3)?\nIf the slope is undefined, type \u003ci\u003e undefined\u003c/i\u003e.\n\u003cbr\u003e\n\u003cspan class=\"ww-blank\" name=\"AnSwEr0002\"\u003e \u003c/span\u003e\n\n\n\u003cbr\u003e\n\nWhat is the slope of the line through (10,\n-10) and (-8,-3)?\nIf the slope is undefined, type \u003ci\u003e undefined\u003c/i\u003e.\n\u003cbr\u003e\n\u003cspan class=\"ww-blank\" name=\"AnSwEr0003\"\u003e \u003c/span\u003e\n\n\n\u003cbr\u003e\n\n\u003c/p\u003e","header_text":{"css":[],"js":[]}}],"instructional":false,"sketchable":true,"print_num_spacing_lines":3,"print_page_break":false,"readonly":{"created_at":"2023-04-17T18:50:18.709Z","updated_at":"2023-04-17T18:50:18.709Z","version":40,"user_id":"58ecdcd48ccf1800120c8ac3","name":"Algorithmic (WebWorK)","skill_ids":["5a134d39c04210000413fb00","5a141e28ac370c0004c76589","5a134d39c04210000413fb00","5a141e28ac370c0004c76589","5a134d39c04210000413fb00","5a141e28ac370c0004c76589","5a134d39c04210000413fb00","5a141e28ac370c0004c76589"],"current_digest":"C1cGW5G28gGRZGmH0UkjD4BCnK7mDQG+55W9yLp508E=","tags":"algebra,lines","points":3.0,"type":"webwork","multipart":true,"shallow":true,"static":true,"sources":[],"owned":false,"url":"/problems/643d94ea84cb430002cd8ed6","searchable_text":"PARWhat is the slope of the line through pts 2 slice k pts 2 slice k 1 and pts 2 slice k 6 pts 2 slice k 7 If the slope is undefined type BITALIC undefined EITALIC ans rule 30 PARWhat is the slope of the line through pts 2 slice k pts 2 slice k 1 and pts 2 slice k 6 pts 2 slice k 7 If the slope is undefined type BITALIC undefined EITALIC ans rule 30 What is the slope of the line through pts 2 slice k pts 2 slice k 1 and pts 2 slice k 6 pts 2 slice k 7 If the slope is undefined type BITALIC undefined EITALIC ans rule 30","abilities":["read"]},"content_license":{"license_type":"OPL","source_url":"https://github.com/Edfinity/webwork-open-problem-library/blob/0914437ac334603bf1f15257757073ac63121956/OpenProblemLibrary/ASU-topics/setLinesInPlane/lines2.pg"}},"readonly":{"shallow":true}}},"readonly":{"level_range":"13","created_at":"2019-02-05T01:45:35.378Z","updated_at":"2024-09-01T18:41:15.729Z","tags":"calculus,oer","author_ids":[],"licensed":true,"thumbnail":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c58eabf4a8e21002b802892/thumb_active-calculus-3.jpg","free":false,"user_price":29.0,"term_price":29.0,"displayed_price":29.0,"levels":"13"},"image":{"url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c58eabf4a8e21002b802892/active-calculus-3.jpg","thumb_url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c58eabf4a8e21002b802892/thumb_active-calculus-3.jpg"}},{"id":"5f16ff9e4a1e8d1366b8f2b1","name":"Active Calculus Multivariable 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If one is not defined, type \u003ci\u003e Undefined \u003c/i\u003e.\n\u003c/p\u003e\n\u003cp\u003e\n\t\\(f(0) =\\)\u003cinput type=\"text\" class=\"codeshard\" size=\"40\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 \" value=\"\"\u003e\u003cinput type=\"hidden\" name=\"previous_AnSwEr0001\" value=\"\"\u003e\u003cbr\u003e\\(f(-5) =\\)\u003cinput type=\"text\" class=\"codeshard\" size=\"40\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 \" value=\"\"\u003e\u003cinput type=\"hidden\" name=\"previous_AnSwEr0002\" value=\"\"\u003e\u003cbr\u003e\\(f(1/3) =\\)\u003cinput type=\"text\" class=\"codeshard\" size=\"40\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 \" value=\"\"\u003e\u003cinput type=\"hidden\" name=\"previous_AnSwEr0003\" value=\"\"\u003e\u003c/p\u003e","static_html":"\u003cp style=\"margin: 0\"\u003e(1 point) Let\n\\[f(x) = \\frac{x+9}{3x-1} .\\]\n\t\nCompute the following values.  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It comprises algorithmic problems carefully organized into problem sets mapped to textbook sections. Use this course as-is, or customize at any level. You can mix-and-match problems from other catalog courses, add problems from the Edfinity problem repository, or write your own.\u003c/p\u003e\u003cp dir=\"ltr\"\u003e\u003cstrong\u003eHow to use this course\u003c/strong\u003e\u003c/p\u003e\u003col\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eHomework\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Assign high quality problems with hints and personalized feedback to develop problem-solving skills.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eTesting\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Create summative secure online quizzes and tests in minutes.\u0026nbsp;\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eSupplementary resources:\u003c/strong\u003e Embed videos, class notes, and applets alongside assignments.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eIntervention:\u003c/strong\u003e Use rich analytics to identify and monitor at-risk students for timely intervention.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eAnalytics:\u003c/strong\u003e Drill down into student performance and identify problematic or difficult topics.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eFlipped classroom:\u003c/strong\u003e Assign pre-class assignments. 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It can be paired with that textbook or with any other commercial or OER Finite Math textbook. It comprises of algorithmic problems carefully organized into problem sets mapped to textbook sections. Use this course as-is, or customize at any level. You can mix-and-match problems from other catalog courses, add problems from the Edfinity problem repository, or write your own.\u003c/p\u003e\u003cp dir=\"ltr\"\u003e\u003cstrong\u003eHow to use this course\u003c/strong\u003e\u003c/p\u003e\u003col\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eHomework\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Assign high quality problems with hints and personalized feedback to develop problem-solving skills.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eTesting\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Create summative secure online quizzes and tests in minutes.\u0026nbsp;\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eSupplementary resources:\u003c/strong\u003e Embed videos, class notes, and applets alongside assignments.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eIntervention:\u003c/strong\u003e Use rich analytics to identify and monitor at-risk students for timely intervention.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eAnalytics:\u003c/strong\u003e Drill down into student performance and identify problematic or difficult topics.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eFlipped classroom:\u003c/strong\u003e Assign pre-class assignments. Save precious class time for discussions.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eEmporium classes:\u003c/strong\u003e Use Edfinity for individual/group work for large enrollment sections in labs.\u003c/li\u003e\u003c/ol\u003e","description_more":"","price":29.0,"sort_order":0,"active":true,"individual_license":false,"section_id":"5ecfd1d0a8836810e87f3568","permissive_license":false,"type":"course","section_license":true,"taxable":false,"purchasable":true,"related_product_ids":[],"audience":"educator_audience","site_ids":["55843bd46435650003000000"],"show_toc":true,"author_roles":[],"author_role_title":"Contributors","tags_array":["business_math","finite_math","discrete_math"],"hidden_tags":["oer"],"term_pricing":true,"curricula":"Texas","curricula_course":"MATH_1324","highlights":"\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-subscript fa-fw mr-2\"\u003e\u003c/i\u003e \u003cstrong\u003eInteractive, algorithmic problems\u003cbr\u003e\u003c/strong\u003eAlgebraic, graphing, open response; randomized variants, hints, and tips\u003c/div\u003e\n\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-hand-holding-heart fa-fw mr-2\"\u003e\u003c/i\u003e\u003cstrong\u003eAdaptive learning and personalization\u003cbr\u003e\u003c/strong\u003eEach student receives personalized support\u003cbr\u003eto fill learning gaps.\u003c/div\u003e\n\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-fw fa-code-branch mr-2\"\u003e\u003c/i\u003e\u003cstrong\u003eCorequisite course structures\u003cbr\u003e\u003c/strong\u003eUse pre-built corequisite content,\u003cbr\u003eor create your own.\u003c/div\u003e\n\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-hands-helping fa-fw mr-2\"\u003e\u003c/i\u003e\u003cstrong\u003eLMS integration and accessibility\u003cbr\u003e\u003c/strong\u003eConnect to your LMS in minutes. \u003ca class=\"”underline”\" href=\"http://edfinity.com/vpat\" target=\"_blank\"\u003eVPAT here\u003c/a\u003e.\u003c/div\u003e\n\u003cdiv class=\"mb-3\"\u003e\u003ci class=\"fa fa-plug fa-fw mr-2\"\u003e\u003c/i\u003e\u003cstrong\u003eWeBWorK-compatible\u003cbr\u003e\u003c/strong\u003eImport and author WeBWorK problems.\u003c/div\u003e\n","preview_assignment":{"id":"5ecfd1d0a8836810e87f3570","name":"Linear Equations","product":{"id":"5edd37e1245cb54de01b1c1d","name":"Applied Finite Mathematics (MATH 1324)"},"master_set":{"id":"675c60fae79d710002cd8bf0","problems":{"id":"6362c3f83745640004518429","proof":false,"graphical_geometric":false,"tags_array":[],"skill_ids":[],"contest_event_ids":[],"header":"","solution":"","part_attributes":[{"id":"5db62425b3e50836ab65eb12","part_id":"5db62425b3e50836ab65eb11","description":null,"points":2.0,"automatic_manual_credit":true,"format":"ww","pg":"## © 2019 Looking Glass Ventures (\"Edfinity\"). All rights reserved. \n## Unauthorized use including modification, sharing, copying is not permitted. \n## For additional information and/or permission to use, write to support@edfinity.com\n\n## DESCRIPTION\n## Find a linear equation, then graph it using GeoGebra\n## A point and slope are given\n## GGB Source: https://www.geogebra.org/classic/m9bqc6s8\n## ENDDESCRIPTION\n\n## DBsubject('College Algebra')\n## Author('Richard G. Lynch')\n\n################################################################################\n#  Initialization\n################################################################################\n\nDOCUMENT();\n\nloadMacros(\n    \"PGstandard.pl\",\n    \"MathObjects.pl\",\n    \"PGML.pl\",\n    \"contextFraction.pl\",\n    \"contextArbitraryString.pl\",\n);\n\nTEXT(beginproblem());\n\n################################################################################\n#  Problem Setup\n################################################################################\n\nContext(\"Fraction\");\nContext()-\u003enoreduce('(-x)-y');\nContext()-\u003enoreduce('(-x)-y','(-x)+y');\n\ndo { # make sure the y-int stays in the graphing area\n    $x = non_zero_random(-6,6);\n    do {$y = non_zero_random(-6,6)} until (abs($y) != abs($x));\n    $pm = non_zero_random(-1,1);\n    $disppm = ($pm \u003e 0) ? \"\" : \"-\";\n    do {\n        $mt = random(1,6);\n        $mb = random(2,7);\n    } until (gcd($mt,$mb) == 1);\n\n    $m = $pm*$mt/$mb;\n    $mfrac = Fraction($pm*$mt,$mb)-\u003ereduce;\n    $b = Fraction($y,1) - $mfrac*Fraction($x,1);\n} until (abs($b) \u003c= 6.5 \u0026\u0026 abs($b \u003e= 0.25));\n\n$line = Formula(\"$mfrac*x + $b\")-\u003ereduce;\n\nContext(\"ArbitraryString\");\n$geogebraChecker = sub {\n  my ($correct,$student,$ansHash) = @_;\n  my @values = split(';', $student-\u003evalue);\n  return $values[-1] == '1' ? 1 : 0;\n};\n$ans = String('1')-\u003ecmp(checker =\u003e $geogebraChecker);\n\n$graph =\n\"\u003cdiv id='ggb' class='ww-ggb'\u003e\u003c/div\u003e\n\n\u003cscript\u003e\n\n    var onLoad = function(applet) {\n        this.setCoordinates('AnSwEr0002', { A:'(-1,-1)', B:'(1,1)'});\n        applet.evalCommand('corrans: {$m,$b}');\n        applet.enableShiftDragZoom(false);\n        applet.enableLabelDrags(false);\n        applet.enableRightClick(false);\n    }\n\n    var onUpdate = function(obj) {\n        this.setCoordinateAnswer('AnSwEr0002', ['A', 'B'], 'check');\n    }\n\n    ggb64 = '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   wwG = new WwGgbApplet('ggb', {height:570, width:570, borderColor:'#FFFFFF', 'ggbBase64':ggb64, appletOnLoad: onLoad, appletOnUpdate: onUpdate, hideAnswers: true});\n\n\u003c/script\u003e\";\n\n\n################################################################################\n#  Text\n################################################################################\n\nBEGIN_PGML\n\na. Find the equation of the line passing through the point [`([$x],[$y])`] with\nslope [`[$disppm]\\dfrac{[$mt]}{[$mb]}`].\n\n        [`y = `] [__]{$line}{width=\u003e20}\n\nb. Graph the line found in Part a. 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You can adjust its position by dragging\naround the points in 1/2 increments.\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv id=\"ggb\" class=\"ww-ggb\"\u003e\u003c/div\u003e\n\n\u003cscript\u003e\n\n    var onLoad = function(applet) {\n        this.setCoordinates('AnSwEr0002', { A:'(-1,-1)', B:'(1,1)'});\n        applet.evalCommand('corrans: {-0.5,(7/2)}');\n        applet.enableShiftDragZoom(false);\n        applet.enableLabelDrags(false);\n        applet.enableRightClick(false);\n    }\n\n    var onUpdate = function(obj) {\n        this.setCoordinateAnswer('AnSwEr0002', ['A', 'B'], 'check');\n    }\n\n    ggb64 = 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name=\"AnSwEr0001\"\u003e \u003c/span\u003e\n\n\u003c/div\u003e\n\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eGraph the line found in Part a. You can adjust its position by dragging\naround the points in 1/2 increments.\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cdiv id=\"ggb\" class=\"ww-ggb\"\u003e\u003c/div\u003e\n\n \u003cspan class=\"ww-blank\" name=\"AnSwEr0002\"\u003e \u003c/span\u003e\n\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e","header_text":{"css":[],"js":[],"inlinejs":[]}}],"instructional":false,"sketchable":true,"print_num_spacing_lines":3,"print_page_break":false,"readonly":{"created_at":"2022-11-02T19:24:40.363Z","updated_at":"2022-11-02T19:24:40.363Z","version":11,"user_id":"58ecdcd48ccf1800120c8ac3","name":"Algorithmic (WebWorK)","skill_ids":[],"current_digest":"UDpLw/FEBOGT+0yqPFSvvd2dO6ZwpnXZ1P7ZrJWnvF4=","tags":"","points":2.0,"type":"webwork","multipart":true,"shallow":true,"static":true,"sources":[],"owned":false,"url":"/problems/6362c3f83745640004518429","searchable_text":"a Find the equation of the line passing through the point x y withslope disppm dfrac mt mb y line width 20 b Graph the line found in Part a You can adjust its position by draggingaround the points in 1 2 increments graph ans SOLUTION Use point slope form to find the equation of the line","abilities":["read"]}},"readonly":{"shallow":true}}},"readonly":{"level_range":"13","created_at":"2020-06-07T18:54:25.088Z","updated_at":"2024-12-13T16:29:54.155Z","tags":"business_math,finite_math,discrete_math","author_ids":[],"licensed":true,"thumbnail":"https://d2b8iahp55539n.cloudfront.net/assets/course-placeholder-3870b2677a589ef8debd801ef338e9403ad9236f1e4562739f9efbd8e456503c.webp","free":false,"user_price":29.0,"term_price":29.0,"displayed_price":29.0,"levels":"13"}}]}