qu.1.topic=Functions (Domain, Types, Shifting)@

qu.1.1.mode=Inline@
qu.1.1.name=Domain and Range (Absolute Value)@
qu.1.1.comment=<p>Here is the original graph, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>y</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup></mrow></mstyle></math>with the function $func.</p>
<p>&nbsp;</p>
<p>$n</p>@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$a=range(1,4);
$b=range(-3,-1);
$func="abs(x+$a)$b";
$m=maple("MathML[ExportPresentation]($func)");
$p=plotmaple("
p1 := plots[implicitplot]({seq(x=i, i=-6..3)}, x=-6..3, y=-5..7, colour=grey):
p2 := plots[implicitplot]({seq(y=i, i=-6..7)}, x=-6..3, y=-5..7, colour=grey):
p3 := plot($func,x=-6..3,y=-5..7, thickness=2):
plots[display]({p1,p2,p3}), plotoptions='width=250, height=250'
");
$n=plotmaple("
p1 := plots[implicitplot]({seq(x=i, i=-6..3)}, x=-6..3, y=-5..7, colour=grey):
p2 := plots[implicitplot]({seq(y=i, i=-6..7)}, x=-6..3, y=-5..7, colour=grey):
p3 := plot($func,x=-6..3,y=-4..7, thickness=2):
p4 := plot(abs(x),x=-6..3,y=-4..7, thickness=3,colour=blue):
plots[display]({p1,p2,p3,p4}), plotoptions='height=250, width=250'
");
$ANSD='"(-infinity,infinity)"';
$ANSR='"[$b,infinity)"';@
qu.1.1.uid=5236505a-dfbf-43fd-9683-8b7a20fa07ab@
qu.1.1.weighting=1,1,1@
qu.1.1.numbering=alpha@
qu.1.1.part.1.name=sro_id_1@
qu.1.1.part.1.maple_answer=abs(x+$a)$b@
qu.1.1.part.1.editing=useHTML@
qu.1.1.part.1.question=(Unset)@
qu.1.1.part.1.libname=@
qu.1.1.part.1.mode=Maple@
qu.1.1.part.1.allow2d=1@
qu.1.1.part.1.plot=@
qu.1.1.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.1.part.1.type=formula@
qu.1.1.part.2.name=sro_id_2@
qu.1.1.part.2.maple_answer=show($ANSD)@
qu.1.1.part.2.editing=useHTML@
qu.1.1.part.2.question=(Unset)@
qu.1.1.part.2.libname=__BASE_URI__Library_Intervals/intervalsLib.lib@
qu.1.1.part.2.mode=Maple@
qu.1.1.part.2.allow2d=0@
qu.1.1.part.2.plot=@
qu.1.1.part.2.maple=grade("$RESPONSE",$ANSD)@
qu.1.1.part.2.type=maple@
qu.1.1.part.3.name=sro_id_3@
qu.1.1.part.3.maple_answer=show($ANSR)@
qu.1.1.part.3.editing=useHTML@
qu.1.1.part.3.question=(Unset)@
qu.1.1.part.3.libname=__BASE_URI__Library_Intervals/intervalsLib.lib@
qu.1.1.part.3.mode=Maple@
qu.1.1.part.3.allow2d=0@
qu.1.1.part.3.plot=@
qu.1.1.part.3.maple=grade("$RESPONSE",$ANSR)@
qu.1.1.part.3.type=maple@
qu.1.1.question=<p>Determine the function, its natural domain, and range from its given graph. (for <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mi>&infin;</mi></mrow></mrow></mstyle></math> or <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&infin;</mi></mrow></mstyle></math> use -infinity and infinity respectively).</p><p>$p</p><p>Hint: The function is based on shifts and/or reflections of the function <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>f</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfenced open='&LeftBracketingBar;' close='&RightBracketingBar;' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p><p><strong>Enter abs(x+1) for | <em>x + </em>1 |.</strong></p><p>&nbsp;f(x) = <span>&nbsp;</span><1><span>&nbsp;</span></p><p><span>&nbsp;For the domain and range, enter your answer in interval notation. For example if 0 &le; x < &infin;, enter [0, infinity).</span></p><p><span>What is the domain of the function?</span></p><p><span><span>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; </span><2><span>&nbsp;</span></span></p><p><span>What is the range of the function?</span></p><p><span><span>&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp; </span><3><span>&nbsp;</span></span></p>@

qu.1.2.mode=Inline@
qu.1.2.name=Growth Rate (Quadratic)@
qu.1.2.comment=<p>Here is a plot of the function <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>r</mi><mfenced open='(' close=')' separators=','><mrow><mi>t</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mn>1</mn><mrow><mn>50</mn></mrow></mfrac><msup><mfenced open='(' close=')' separators=','><mrow><mi>t</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>20</mn></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>8</mn></mrow></mstyle></math>.</p>
<p>&nbsp;</p>
<p>$p</p>@
qu.1.2.editing=useHTML@
qu.1.2.solution=@
qu.1.2.algorithm=$func="(-1/50)*(t-20)^2+8";
$m=maple("MathML[ExportPresentation]($func)");
$p=plotmaple("
p1 := plots[implicitplot]({seq(t=i, i=0..40)}, t=-0..40, y=0..10, colour=grey):
p2 := plots[implicitplot]({seq(y=i, i=0..40)}, t=0..40, y=0..10, colour=grey):
p3 := plot($func,t=0..40,y=0..10, discont=true, thickness=2):
plots[display]({p1,p2,p3}), plotoptions='height=250, width=250'
");@
qu.1.2.uid=7a6c1648-c7d3-4e45-80aa-f4d7b2dbe79c@
qu.1.2.weighting=1@
qu.1.2.numbering=alpha@
qu.1.2.part.1.name=sro_id_1@
qu.1.2.part.1.editing=useHTML@
qu.1.2.part.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>r</mi><mfenced open='(' close=')' separators=','><mrow><mi>t</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mn>2</mn><mrow><mn>5</mn></mrow></mfrac><msup><mfenced open='(' close=')' separators=','><mrow><mi>t</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>20</mn></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>8</mn></mrow></mstyle></math>@
qu.1.2.part.1.fixed=@
qu.1.2.part.1.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>r</mi><mfenced open='(' close=')' separators=','><mrow><mi>t</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mn>1</mn><mrow><mn>50</mn></mrow></mfrac><msup><mfenced open='(' close=')' separators=','><mrow><mi>t</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>20</mn></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>8</mn></mrow></mstyle></math>@
qu.1.2.part.1.question=null@
qu.1.2.part.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>r</mi><mfenced open='(' close=')' separators=','><mrow><mi>t</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mn>2</mn><mrow><mn>5</mn></mrow></mfrac><msup><mfenced open='(' close=')' separators=','><mrow><mi>t</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>20</mn></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>8</mn></mrow></mstyle></math>@
qu.1.2.part.1.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>r</mi><mfenced open='(' close=')' separators=','><mrow><mi>t</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mn>1</mn><mrow><mn>50</mn></mrow></mfrac><msup><mfenced open='(' close=')' separators=','><mrow><mi>t</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>40</mn></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>8</mn></mrow></mstyle></math>@
qu.1.2.part.1.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>r</mi><mfenced open='(' close=')' separators=','><mrow><mi>t</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mn>1</mn><mrow><mn>50</mn></mrow></mfrac><msup><mfenced open='(' close=')' separators=','><mrow><mi>t</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>20</mn></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>8</mn></mrow></mstyle></math>@
qu.1.2.part.1.mode=Multiple Choice@
qu.1.2.part.1.display=vertical@
qu.1.2.part.1.answer=4@
qu.1.2.question=<p>Assume that the growth rate of a plant, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>r</mi><mfenced open='(' close=')' separators=','><mrow><mi>t</mi></mrow></mfenced></mrow></mstyle></math>, is a quadratic function of the number of days, t, since the seed was sown.&nbsp; If the plant is not growing at seeding and ceases to grow after 40 days, and if the plant's maximum growth rate is a 8cm/day then <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>r</mi><mfenced open='(' close=')' separators=','><mrow><mi>t</mi></mrow></mfenced></mrow></mstyle></math> is given by:</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.3.mode=Inline@
qu.1.3.name=Domain - Floor function ii@
qu.1.3.comment=<p>Note the difference between <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>a</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>b</mi></mrow></mfenced></mrow></mstyle></math> and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='[' close=')' separators=','><mrow><mi>a</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>b</mi></mrow></mfenced></mrow></mstyle></math>. The graph looks like this!</p>
<p>$p</p>@
qu.1.3.editing=useHTML@
qu.1.3.solution=@
qu.1.3.algorithm=$a=range(4,6);
$b=$a*$a;
$m=maple("
func:=sqrt($b-x^2)/floor(x):
disp:=MathML[ExportPresentation](func):
convert(func,string),disp
");
$func=switch(0,$m);
$disp=switch(1,$m);
$p=plotmaple("
p1 := plot($func, x = -5..-0.1, y = -6..6, discont = [usefdiscont = [bins = 45]]):
p2 := plot($func, x = 1..6, y = -6..6, discont = [usefdiscont = [bins = 45]]):
plots[display]({p1,p2})
");@
qu.1.3.uid=1b505da6-158e-4eb5-a467-dd628d45e9f6@
qu.1.3.weighting=1@
qu.1.3.numbering=alpha@
qu.1.3.part.1.name=sro_id_1@
qu.1.3.part.1.editing=useHTML@
qu.1.3.part.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='[' close=']' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$a</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>0</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&cup;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='(' close=']' separators=','><mrow><mn>1</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$a</mi></mrow></mfenced></mrow></mstyle></math>@
qu.1.3.part.1.fixed=@
qu.1.3.part.1.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$a</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>0</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&cup;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='[' close=')' separators=','><mrow><mn>1</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$a</mi></mrow></mfenced></mrow></mstyle></math>@
qu.1.3.part.1.question=null@
qu.1.3.part.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='[' close=')' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$a</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>0</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&cup;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='[' close=']' separators=','><mrow><mn>1</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$a</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math>@
qu.1.3.part.1.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=']' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&infin;</mo><mo mathvariant='italic' separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$a</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&cup;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='[' close=')' separators=','><mrow><mi>$a</mi><mo mathvariant='italic' separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&infin;</mo></mrow></mfenced></mrow></mstyle></math>@
qu.1.3.part.1.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='[' close=']' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$a</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>0</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&cup;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='[' close=']' separators=','><mrow><mn>1</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$a</mi></mrow></mfenced></mrow><mrow></mrow></mstyle></math>@
qu.1.3.part.1.mode=Multiple Choice@
qu.1.3.part.1.display=vertical@
qu.1.3.part.1.answer=3@
qu.1.3.question=<p>The natural domain of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>f</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><msqrt><mrow><mi>$b</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup></mrow></msqrt><mrow><mfenced open='&lobrk;' close='&robrk;' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mfrac></mrow></mrow></mstyle></math> is</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.4.mode=Inline@
qu.1.4.name=Domain and Range (Quadratic)@
qu.1.4.comment=<p>Here is the original graph, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>y</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup></mrow></mstyle></math>with the function y = $m.</p>
<p>&nbsp;</p>
<p>$n</p>@
qu.1.4.editing=useHTML@
qu.1.4.solution=@
qu.1.4.algorithm=$a=range(1,5);
$func="(x-($a))^2";
$m=maple("MathML[ExportPresentation]($func)");
$p=plotmaple("
p1 := plots[implicitplot]({seq(x=i, i=-3..8)}, x=-3..8, y=-4..7, colour=grey):
p2 := plots[implicitplot]({seq(y=i, i=-3..8)}, x=-3..8, y=-4..7, colour=grey):
p3 := plot($func,x=-3..8,y=-4..7, thickness=2):
plots[display]({p1,p2,p3}), plotoptions='height=250, width=250'
");
$n=plotmaple("
p1 := plots[implicitplot]({seq(x=i, i=-3..8)}, x=-3..8, y=-4..7, colour=grey):
p2 := plots[implicitplot]({seq(y=i, i=-3..8)}, x=-3..8, y=-4..7, colour=grey):
p3 := plot($func,x=-3..8,y=-4..7, thickness=2):
p4 := plot(x^2,x=-3..8,y=-4..7, thickness=2,colour=blue):
plots[display]({p1,p2,p3,p4}), plotoptions='height=250, width=250'
");
$ANSD = '"(-infinity,infinity)"';
$ANSR = '"[0,infinity)"';@
qu.1.4.uid=f237750b-0d74-427a-9860-c4fbc26097b5@
qu.1.4.weighting=1,1,1@
qu.1.4.numbering=alpha@
qu.1.4.part.1.name=sro_id_1@
qu.1.4.part.1.maple_answer=(x-($a))^2@
qu.1.4.part.1.editing=useHTML@
qu.1.4.part.1.question=(Unset)@
qu.1.4.part.1.libname=@
qu.1.4.part.1.mode=Maple@
qu.1.4.part.1.allow2d=1@
qu.1.4.part.1.plot=@
qu.1.4.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.4.part.1.type=formula@
qu.1.4.part.2.name=sro_id_2@
qu.1.4.part.2.maple_answer=show($ANSD)@
qu.1.4.part.2.editing=useHTML@
qu.1.4.part.2.question=(Unset)@
qu.1.4.part.2.libname=__BASE_URI__Library_Intervals/intervalsLib.lib@
qu.1.4.part.2.mode=Maple@
qu.1.4.part.2.allow2d=0@
qu.1.4.part.2.plot=@
qu.1.4.part.2.maple=grade("$RESPONSE",$ANSD);@
qu.1.4.part.2.type=maple@
qu.1.4.part.3.name=sro_id_3@
qu.1.4.part.3.maple_answer=show($ANSR)@
qu.1.4.part.3.editing=useHTML@
qu.1.4.part.3.question=(Unset)@
qu.1.4.part.3.libname=__BASE_URI__Library_Intervals/intervalsLib.lib@
qu.1.4.part.3.mode=Maple@
qu.1.4.part.3.allow2d=0@
qu.1.4.part.3.plot=@
qu.1.4.part.3.maple=mark:=grade("$RESPONSE",$ANSR);
if (grade("$RESPONSE","(0,infinity]")) then
mark:=0.5;
end if;
mark@
qu.1.4.part.3.type=maple@
qu.1.4.question=<p>Determine the function, its natural domain, and range from its given graph. (for <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mi>&infin;</mi></mrow></mrow></mstyle></math> or <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&infin;</mi></mrow></mstyle></math> use -infinity and infinity respectively).</p><p>$p</p><p>Hint: The function is based on shifts and/or reflections of the function <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>f</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup></mrow></mstyle></math></p><p>&nbsp;f(x) = <span>&nbsp;</span><1><span>&nbsp;</span></p><p><span>For the domain &amp; range, enter your answer in interval notation. For example if 0 &le; x < &infin;, enter [0, infinity).<br /></span></p><p><span>What is the domain of the function?</span></p><p><span><span>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; </span><2><span>&nbsp;</span></span></p><p><span>What is the range of the function?</span></p><p><span><span>&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp; </span><3><span>&nbsp;</span></span></p>@

qu.1.5.mode=Inline@
qu.1.5.name=Domain - Floor Function i@
qu.1.5.comment=<p>Note the difference between <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>a</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>b</mi></mrow></mfenced></mrow></mstyle></math> and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='[' close=')' separators=','><mrow><mi>a</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>b</mi></mrow></mfenced></mrow></mstyle></math>.&nbsp;&nbsp;</p>
<p>The graph looks like this!</p>
<p>$plot</p>@
qu.1.5.editing=useHTML@
qu.1.5.solution=@
qu.1.5.algorithm=$a=range(4,9);
$m=maple("
func:=sqrt($a-x)/floor(x):
disp:=MathML[ExportPresentation](func):
convert(func,string),disp
");
$func=switch(0,$m);
$disp=switch(1,$m);
$plot=plotmaple("plot($func,discont = [usefdiscont = [bins = 35]])");@
qu.1.5.uid=3ee33c41-3379-464e-9e07-cf63a994e918@
qu.1.5.weighting=1@
qu.1.5.numbering=alpha@
qu.1.5.part.1.name=sro_id_1@
qu.1.5.part.1.editing=useHTML@
qu.1.5.part.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='[' close=')' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$a</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>0</mn></mrow></mfenced><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&cup;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='[' close=')' separators=','><mrow><mn mathvariant='italic'>1</mn><mo mathvariant='italic' separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&infin;</mo></mrow></mfenced></mrow></mstyle></math>@
qu.1.5.part.1.fixed=@
qu.1.5.part.1.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&infin;</mo><mo mathvariant='italic' separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn mathvariant='italic'>0</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&cup;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='(' close=']' separators=','><mrow><mn>1</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$a</mi></mrow></mfenced></mrow></mstyle></math>@
qu.1.5.part.1.question=null@
qu.1.5.part.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='[' close=')' separators=','><mrow><mi>$a</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&infin;</mo></mrow></mfenced></mrow></mstyle></math>@
qu.1.5.part.1.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&infin;</mo><mo mathvariant='italic' separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn mathvariant='italic'>0</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&cup;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='[' close=']' separators=','><mrow><mn>1</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$a</mi></mrow></mfenced></mrow></mstyle></math>@
qu.1.5.part.1.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=']' separators=','><mrow><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&infin;</mo><mo mathvariant='italic' separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn mathvariant='italic'>0</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&cup;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='(' close=']' separators=','><mrow><mn>1</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$a</mi></mrow></mfenced></mrow><mrow></mrow></mstyle></math>@
qu.1.5.part.1.mode=Multiple Choice@
qu.1.5.part.1.display=vertical@
qu.1.5.part.1.answer=2@
qu.1.5.question=<p>The natural domain of&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><msqrt><mrow><mi>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mi>x</mi></mrow></mrow></msqrt><mrow><mfenced open='&lobrk;' close='&robrk;' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math> (where <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='&lobrk;' close='&robrk;' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mstyle></math> is the greatest integer of x) is</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.6.mode=Inline@
qu.1.6.name=Domain and Range (x^1/3)@
qu.1.6.comment=<p>Here is the graph of the base function y = x<sup>1/3</sup>, with the function $func.</p>
<p>&nbsp;$n</p>@
qu.1.6.editing=useHTML@
qu.1.6.solution=@
qu.1.6.algorithm=$a=range(2,4);
$b=range(-3,-1);
$func=maple("surd($b*x,3)+$a");
$dispfunc="$b*x^(1/3)+$a";
$m=maple("MathML[ExportPresentation]($dispfunc)");
$p=plotmaple("
p1 := plots[implicitplot]({seq(x=i, i=-4..6)}, x=-4..6, y=-5..7, colour=grey):
p2 := plots[implicitplot]({seq(y=i, i=-5..7)}, x=-4..6, y=-5..7, colour=grey):
p3 := plot($func,x=-4..6,y=-5..7, thickness=2):
plots[display]({p1,p2,p3}), plotoptions='height=250, width=250'
");
$n=plotmaple("
p1 := plots[implicitplot]({seq(x=i, i=-4..4)}, x=-4..6, y=-5..7, colour=grey):
p2 := plots[implicitplot]({seq(y=i, i=-5..7)}, x=-4..6, y=-5..7, colour=grey):
p3 := plot($func,x=-4..6,y=-5..7, discont=true, thickness=2):
p4 := plot(surd(x,3),x=-4..6,y=-5..7, discont=true,colour=blue,thickness=2):
plots[display]({p1,p2,p3,p4}), plotoptions='height=250, width=250'
");@
qu.1.6.uid=182c27f5-d9a5-4e69-b2ad-0e4ce360158c@
qu.1.6.weighting=1@
qu.1.6.numbering=alpha@
qu.1.6.part.1.name=sro_id_1@
qu.1.6.part.1.editing=useHTML@
qu.1.6.part.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mfrac><mn>1</mn><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mfrac></mrow></msup><mi>$b</mi></mrow></mstyle></math>@
qu.1.6.part.1.fixed=@
qu.1.6.part.1.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$b</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mfrac><mn>1</mn><mrow><mn>3</mn></mrow></mfrac></mrow></msup></mrow></mstyle></math>@
qu.1.6.part.1.question=null@
qu.1.6.part.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mfrac><mn>1</mn><mrow><mn>3</mn></mrow></mfrac></mrow></msup><mi>$b</mi></mrow></mstyle></math>@
qu.1.6.part.1.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mn>3</mn></mrow></msup></mrow></mstyle></math>@
qu.1.6.part.1.choice.1=$m@
qu.1.6.part.1.mode=Multiple Choice@
qu.1.6.part.1.display=vertical@
qu.1.6.part.1.answer=1@
qu.1.6.question=<p>Which one of the following equations represents the sketched graph?</p><p>$p</p><p>&nbsp;<span>&nbsp;</span><1><span>&nbsp;</span></p>@

