## DESCRIPTION ## Algebra - Transformation of Graphs ## ENDDESCRIPTION ## DBsubject(Algebra) ## DBchapter(Transformations of functions and graphs) ## DBsection(Shifts: vertical and horizontal) ## Date(7/17/2022) ## Institution(UWEC) ## Level(2) ## KEYWORDS('Algebra','Transformtions','Graphs','transformations of functions') # # First comes some stuff that appears at the beginning of every problem # DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PGstandard.pl", "MathObjects.pl", "answerHints.pl", "PGtikz.pl", "TikZ_utils.pl", "PGcourse.pl", ); TEXT(beginproblem()); \$refreshCachedImages = 1; #Graph the standard function \$graph=GraphWithTikZ(function=>Formula("x^2")); #pick offsets \$a=non_zero_random(-3,3); do {\$b=non_zero_random(-3, 3)} until abs(\$b)!=abs(\$a); \$c=-\$a; #These are the correct answers \$ans1 = Compute("(x+\$c)**2")->with(limits=>[-5,5]); \$ans2 = Compute("x**2+\$b")->with(limits=>[-5,5]); #prepare graph of first correct answer \$graph1 = GraphWithTikZ(function=>\$ans1); # prepare graph of second correct answer \$graph2 = GraphWithTikZ(function=>\$ans2); BEGIN_TEXT The graph of \( y= x^2 \) is given below: \$BR \{ image(\$graph, width=>200, tex_size=>1000) \} \$BR Find a formula for each of the transformations whose graphs are given below. \$BR a) \$BR \{ image(insertGraph(\$graph1), width=>200, tex_size=>1000) \} \$BR \( y = \) \{ans_rule(30)\} \$BR b) \$BR \{ image(insertGraph(\$graph2), width=>200, tex_size=>1000) \} \$BR \( y = \) \{ans_rule(30)\} END_TEXT ANS(\$ans1->cmp()->withPostFilter(AnswerHints( [Compute("x**2+\$c"),Compute("x**2-\$c")]=>"To get a horizontal shift, f(x-h), you must substitute (x-h) IN PARENTHESES for x in the original function.", Compute("(x+\$a)**2")=>"Be careful of the direction of the shift", ))); ANS(\$ans2->cmp()->withPostFilter(AnswerHints( [Compute("(x+\$b)**2"),Compute("(x-(\$b))**2")]=>"To get a vertical shift, f(x)+k, you must add k to the original function.", Compute("x**2-(\$b)")=>"Be careful of the direction of the shift", )) ); ENDDOCUMENT(); # This should be the last executable line in the problem.