M110 CLASS NOTES

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M110 CLASS NOTES

• SECTION 4.5
• Rational Functions

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A Java Enhanced Web Page
I have developed a collection of web pages for
this topic.
See Graphing Rational Functions by connecting to
my website http//waukesha.uwc.edu/mat/psundhei/
and scrolling down to FILES FOR COLLEGE ALGEBRA
. This URL can be found on the first page of
your syllabus for this course.
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EXAMPLE 1 GRAPH
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EXAMPLE 1 GRAPH
Factor 9 x2 -(x2 9) -(x 3)(x 3)
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EXAMPLE 1 GRAPH
Factor 2x2 5x - 18 (2x 9)(x 2)
2 9 9 1 -2
-4 5
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EXAMPLE 1 GRAPH
Factor 2x2 5x - 18 (2x 9)(x 2)
2 9 9 1 -2
-4 5
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EXAMPLE 1 GRAPH
x-intercepts (set num 0) x ?3
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EXAMPLE 1 GRAPH
x-intercepts x ?3 v-asymtotes (set denom
0) x 2, -9/2
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EXAMPLE 1 GRAPH
x-intercepts x ?3 v-asymtotes x 2, -9/2
-9/2 -3 2
3
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EXAMPLE 1 GRAPH
x-intercepts x ?3 v-asymtotes x 2, -9/2
-9/2 -3 2
3
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EXAMPLE 1 GRAPH
x-intercepts x ?3 v-asymtotes x 2,
-9/2 h-asymptotes y -1/2 (because the degrees
are the same)
-9/2 -3 2
3
-1/2
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EXAMPLE 1 GRAPH
x-intercepts x ?3 v-asymtotes x 2, -9/2
h-asymptotes y -1/2
Finally, from the original form for f(x), f(0)
9/-18 -1/2
-9/2 -3 2
3
-1/2
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EXAMPLE 1 GRAPH
x-intercepts x ?3 v-asymtotes x 2,
-9/2 h-asymptotes y -1/2 (because the degrees
are the same)
-9/2 -3 2
3
-1/2
The graph starts (on the left) near the line y
-1/2
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EXAMPLE 1 GRAPH
x-intercepts x ?3 v-asymtotes x 2,
-9/2 h-asymptotes y -1/2 (because the degrees
are the same)
-9/2 -3 2
3
-1/2
The graph follows near the vertical asymptote
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EXAMPLE 1 GRAPH
x-intercepts x ?3 v-asymtotes x 2,
-9/2 h-asymptotes y -1/2 (because the degrees
are the same)
-9/2 -3 2
3
-1/2
The graph switches to the positive side (because
2x 9 was raised to an odd power)
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EXAMPLE 1 GRAPH
x-intercepts x ?3 v-asymtotes x 2,
-9/2 h-asymptotes y -1/2 (because the degrees
are the same)
-9/2 -3 2
3
-1/2
The graph crosses through x -3 (because x 3
was raised to an odd power)
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EXAMPLE 1 GRAPH
x-intercepts x ?3 v-asymtotes x 2,
-9/2 h-asymptotes y -1/2 (because the degrees
are the same)
-9/2 -3 2
3
-1/2
The graph draws near the v-axymp. x 2
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EXAMPLE 1 GRAPH
x-intercepts x ?3 v-asymtotes x 2,
-9/2 h-asymptotes y -1/2 (because the degrees
are the same)
-9/2 -3 2
3
-1/2
The graph moves to the other side of the x-axis
because x 2 was raised to an odd power.
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EXAMPLE 1 GRAPH
x-intercepts x ?3 v-asymtotes x 2,
-9/2 h-asymptotes y -1/2 (because the degrees
are the same)
-9/2 -3 2
3
-1/2
The graph crosses at x 3, because x 3 was
raised to an odd power.
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EXAMPLE 1 GRAPH
x-intercepts x ?3 v-asymtotes x 2,
-9/2 h-asymptotes y -1/2 (because the degrees
are the same)
-9/2 -3 2
3
-1/2
The graph gets close to the line y -1/2..
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End of Section 4.5