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merged 14 commits into from
Dec 17, 2024
Merged

Appendix of common graphs #416

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e1564d1
First graph
siwelwerd Nov 12, 2024
7a81767
Update source/precalculus/source/meta/graphs.ptx
siwelwerd Nov 12, 2024
8675102
Update source/precalculus/source/meta/graphs.ptx
siwelwerd Nov 15, 2024
3fd9dcf
Reformat as sidebyside
siwelwerd Nov 15, 2024
1b0d170
Add rational functions
siwelwerd Nov 15, 2024
4f5f2ab
Fix captions
siwelwerd Nov 19, 2024
ecc8d29
Other graphs
siwelwerd Nov 19, 2024
29b5977
Exponential and logarithmic graphs
siwelwerd Nov 19, 2024
ad0ee12
Trigonometric functions
siwelwerd Nov 19, 2024
622636a
Inverse trig functions
siwelwerd Nov 19, 2024
7e2ec51
Add asymptotes
siwelwerd Nov 19, 2024
fd13443
Add xml:ids
siwelwerd Nov 19, 2024
35b0f3a
Reorder appendices
siwelwerd Nov 19, 2024
fe0cee0
Merge branch 'main' into precalculus-graphs-appendix
StevenClontz Dec 17, 2024
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1 change: 1 addition & 0 deletions source/precalculus/source/meta/backmatter.ptx
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<backmatter xmlns:xi="http://www.w3.org/2001/XInclude" xml:id="backmatter">
<title>Backmatter</title>

<xi:include href="graphs.ptx"/>
<xi:include href="identities.ptx"/>

<!-- <solutions divisional="hint"> <title>Selected Hints</title> </solutions> -->
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282 changes: 282 additions & 0 deletions source/precalculus/source/meta/graphs.ptx
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@@ -0,0 +1,282 @@
<?xml version='1.0' encoding='UTF-8'?>
<appendix xml:id="graphs-of-common-functions" xmlns:xi="http://www.w3.org/2001/XInclude">
<title>Graphs of Common Functions</title>
<paragraphs xml:id="polynomial-functions-graphs">
<title>Polynomial Functions</title>
<p>
<sbsgroup>
<sidebyside>
<figure xml:id="graph-x">
<image><sageplot>
plot(x,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,gridlines=True, ticks=[1,1])
</sageplot></image>
<caption>Graph of <m>y=x</m></caption>
</figure>
<figure xml:id="graph-x-squared">
<image><sageplot>
plot(x^2,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,gridlines=True, ticks=[1,1])
</sageplot></image>
<caption>Graph of <m>y=x^2</m></caption>
</figure>
</sidebyside>
<sidebyside>
<figure xml:id="graph-x-cubed">
<image><sageplot>
plot(x^3,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,gridlines=True, ticks=[1,1])
</sageplot></image>
<caption>Graph of <m>y=x^3</m></caption>
</figure>
<figure xml:id="graph-x-fourth">
<image><sageplot>
plot(x^4,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,gridlines=True, ticks=[1,1])
</sageplot></image>
<caption>Graph of <m>y=x^4</m></caption>
</figure>
</sidebyside>
</sbsgroup>
</p>
</paragraphs>
<paragraphs xml:id="rational-functions-graphs">
<title>Rational Functions</title>
<p>
<sbsgroup>
<sidebyside>
<figure xml:id="graph-x-minus-one">
<image><sageplot>
p=plot(1/x,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1])
p+=line([(0,-5),(0,5)],thickness=3,linestyle='dashed',color='red')
p+=line([(-5,0),(5,0)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=\dfrac{1}{x}</m></caption>
</figure>
<figure xml:id="graph-x-minus-2">
<image><sageplot>
p=plot(1/x^2,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1])
p+=line([(0,-5),(0,5)],thickness=3,linestyle='dashed',color='red')
p+=line([(-5,0),(5,0)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=\dfrac{1}{x^2}</m></caption>
</figure>
</sidebyside>
<sidebyside>
<figure xml:id="graph-x-minus-three">
<image><sageplot>
p=plot(1/x^3,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1])
p+=line([(0,-5),(0,5)],thickness=3,linestyle='dashed',color='red')
p+=line([(-5,0),(5,0)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=\dfrac{1}{x^3}</m></caption>
</figure>
<figure xml:id="graph-x-minus-four">
<image><sageplot>
p=plot(1/x^4,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1])
p+=line([(0,-5),(0,5)],thickness=3,linestyle='dashed',color='red')
p+=line([(-5,0),(5,0)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=\dfrac{1}{x^4}</m></caption>
</figure>
</sidebyside>
</sbsgroup>
</p>
</paragraphs>
<paragraphs xml:id="other-functions-graphs">
<title>Other Functions</title>
<p>
<sbsgroup>
<sidebyside>
<figure xml:id="graph-absolute">
<image><sageplot>
plot(abs(x),xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1])
</sageplot></image>
<caption>Graph of <m>y=|x|</m></caption>
</figure>
<figure xml:id="graph-sqrt">
<image><sageplot>
p=plot(sqrt(x),xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1])
p.SHOW_OPTIONS['xmin']=-5
p
</sageplot></image>
<caption>Graph of <m>y=\sqrt{x}</m></caption>
</figure>
</sidebyside>
</sbsgroup>
</p>
</paragraphs>
<paragraphs xml:id="exponential-and-logarithmic-functions-graphs">
<title>Exponential and Logarithmic Functions</title>
<p>
<sbsgroup>
<sidebyside>
<figure xml:id="graph-exponential">
<image><sageplot>
p=plot(2^x,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1])
p+=line([(-5,0),(5,0)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=b^x</m>, with <m>b=2</m></caption>
</figure>
<figure xml:id="graph-log">
<image><sageplot>
p=plot(log(x)/log(2),xmin=0,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1])
p+=line([(0,-5),(0,5)],thickness=3,linestyle='dashed',color='red')
p.SHOW_OPTIONS['xmin']=-5
p
</sageplot></image>
<caption>Graph of <m>y=\log_b x</m>, with <m>b=2</m></caption>
</figure>
</sidebyside>
<sidebyside>
<figure xml:id="graph-e">
<image><sageplot>
p=plot(e^x,xmin=-5,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1])
p+=line([(-5,0),(5,0)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=e^x</m></caption>
</figure>
<figure xml:id="graph-ln">
<image><sageplot>
p=plot(log(x),xmin=0,xmax=5,ymin=-5,ymax=5,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,1])
p+=line([(0,-5),(0,5)],thickness=3,linestyle='dashed',color='red')
p.SHOW_OPTIONS['xmin']=-5
p
</sageplot></image>
<caption>Graph of <m>y=\ln x</m></caption>
</figure>
</sidebyside>
</sbsgroup>
</p>
</paragraphs>
<paragraphs xml:id="trigonometric-functions-graphs">
<title>Trigonometric Functions</title>
<p>
<sbsgroup>
<sidebyside>
<figure xml:id="graph-sin">
<image><sageplot>
plot(sin(x),xmin=-2*pi,xmax=2*pi,ymin=-2*pi,ymax=2*pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[pi/2,1],tick_formatter=[pi,1])
</sageplot></image>
<caption>Graph of <m>y=\sin(x)</m></caption>
</figure>
<figure xml:id="graph-csc">
<image><sageplot>
p=plot(csc(x),xmin=-2*pi,xmax=2*pi,ymin=-2*pi,ymax=2*pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[pi/2,1],tick_formatter=[pi,1])
for i in [-2..2]:
p+=line([(i*pi,-2*pi),(i*pi,2*pi)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=\csc x</m></caption>
</figure>
</sidebyside>
<sidebyside>
<figure xml:id="graph-cos">
<image><sageplot>
plot(cos(x),xmin=-2*pi,xmax=2*pi,ymin=-2*pi,ymax=2*pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[pi/2,1],tick_formatter=[pi,1])
</sageplot></image>
<caption>Graph of <m>y=\cos x</m></caption>
</figure>
<figure xml:id="graph-sec">
<image><sageplot>
p=plot(sec(x),xmin=-2*pi,xmax=2*pi,ymin=-2*pi,ymax=2*pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[pi/2,1],tick_formatter=[pi,1])
for i in [-2..1]:
p+=line([(i*pi+pi/2,-2*pi),(i*pi+pi/2,2*pi)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=\sec x</m></caption>
</figure>
</sidebyside>
<sidebyside>
<figure xml:id="graph-tan">
<image><sageplot>
p=plot(tan(x),xmin=-2*pi,xmax=2*pi,ymin=-2*pi,ymax=2*pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[pi/2,1],tick_formatter=[pi,1])
for i in [-2..1]:
p+=line([(i*pi+pi/2,-2*pi),(i*pi+pi/2,2*pi)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=\tan x</m></caption>
</figure>
<figure xml:id="graph-cot">
<image><sageplot>
p=plot(cot(x),xmin=-2*pi,xmax=2*pi,ymin=-2*pi,ymax=2*pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[pi/2,1],tick_formatter=[pi,1])
for i in [-2..2]:
p+=line([(i*pi,-2*pi),(i*pi,2*pi)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=\cot x</m></caption>
</figure>
</sidebyside>
</sbsgroup>
</p>
</paragraphs>
<paragraphs xml:id="inverse-trigonometric-functions-graphs">
<title>Inverse Trigonometric Functions</title>
<p>
<sbsgroup>
<sidebyside>
<figure xml:id="graph-arcsin">
<image><sageplot>
p=plot(arcsin(x),xmin=-1,xmax=1,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[1,pi])
p.SHOW_OPTIONS['xmin']=-pi
p.SHOW_OPTIONS['xmax']=pi
p
</sageplot></image>
<caption>Graph of <m>y=\sin^{-1}(x)</m></caption>
</figure>
<figure xml:id="graph-arccsc">
<image><sageplot>
p=plot(arccsc(x),xmin=-pi,xmax=-1,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[1,pi])
p+=plot(arccsc(x),xmin=1,xmax=pi,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[1,pi])
p+=line([(-pi,0),(pi,0)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=\csc^{-1}(x)</m></caption>
</figure>
</sidebyside>
<sidebyside>
<figure xml:id="graph-arccos">
<image><sageplot>
p=plot(arccos(x),xmin=-1,xmax=1,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[1,pi])
p.SHOW_OPTIONS['xmin']=-pi
p.SHOW_OPTIONS['xmax']=pi
p
</sageplot></image>
<caption>Graph of <m>y=\cos^{-1}(x)</m></caption>
</figure>
<figure xml:id="graph-arcsec">
<image><sageplot>
p=plot(arcsec(x),xmin=-pi,xmax=-1,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[1,pi])
p+=plot(arcsec(x),xmin=1,xmax=pi,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[1,pi])
p+=line([(-pi,pi/2),(pi,pi/2)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=\sec^{-1}(x)</m></caption>
</figure>
</sidebyside>
<sidebyside>
<figure xml:id="graph-arctan">
<image><sageplot>
p=plot(arctan(x),xmin=-pi,xmax=pi,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[1,pi])
p+=line([(-pi,pi/2),(pi,pi/2)],thickness=3,linestyle='dashed',color='red')
p+=line([(-pi,-pi/2),(pi,-pi/2)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=\tan^{-1}(x)</m></caption>
</figure>
<figure xml:id="graph-arccot">
<image><sageplot>
p=plot(arccot(x),xmin=-pi,xmax=-0.001,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[1,pi])
p+=plot(arccot(x),xmin=0.001,xmax=pi,ymin=-pi,ymax=pi,thickness=3,aspect_ratio=1,detect_poles=True,gridlines=True, ticks=[1,pi/4],tick_formatter=[1,pi])
p+=line([(-pi,0),(pi,0)],thickness=3,linestyle='dashed',color='red')
p
</sageplot></image>
<caption>Graph of <m>y=\cot^{-1}(x)</m></caption>
</figure>
</sidebyside>
</sbsgroup>
</p>
</paragraphs>
</appendix>
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