5.3 graphing general rational functions.notebook · 2019-09-05 · 5.3 graphing general rational...
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![Page 1: 5.3 Graphing General Rational Functions.notebook · 2019-09-05 · 5.3 Graphing General Rational Functions.notebook May 11, 2015 Bell Work Factor the following expressions. 1) 12x2](https://reader031.vdocuments.us/reader031/viewer/2022040816/5e5e4dfa6119a1165a557527/html5/thumbnails/1.jpg)
5.3 Graphing General Rational Functions.notebook May 11, 2015
Bell Work
Factor the following expressions.
1) 12x2 + 5x 2 2) x2 5x 50
5.3 Graph General Rational FunctionsIn section 5.2 we learned how to graph simple rational functions.
Two Forms:
1. y = ax h + k VA:
HA:
2. y = ax + bcx + dVA:
HA:
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5.3 Graphing General Rational Functions.notebook May 11, 2015
To graph general rational functions we will find 5 things:
* xintercept(s)
* vertical asymptote(s)
* horizontal asymptote
* hole
* point of discontinuity
Points of discontinuity
are moments within a function that are undefined and appear as a break or hole in a graph
created when a function is presented as a fraction and an inputted variable creates a denominator equal to zero
Discontinuities: 1, 3
x intercepts: (0,0), (4,0)
Vertical Asym: x = 1, x=3
Horizontal Asym: y=3
Holes: None
Example
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5.3 Graphing General Rational Functions.notebook May 11, 2015
Discontinuities: 1, 3
x intercepts: (0,0), (4,0)
Vertical Asym: x = 1
Horizontal Asym: none
Holes: (3, 1.5)
Example
x intercept(s)Find the xvalues that make the numerator zero.
Example 1: Find the xintercepts of the function.
x2 + 3x 4y = x 2
_________
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5.3 Graphing General Rational Functions.notebook May 11, 2015
Vertical Asymptotes*Find the xvalues that make the denominator zero.
Example 2: Find all the vertical asymptotes ofa. f(x) =
xx2 + 5x + 6
b. f(x) = x2 4x 12
x2 11x + 30_____________
Horizontal Asymptotes*Find the degree of the numerator and denominator.
Case 1 m < nThe line y = 0
is a horizontal asymptote.
Case 2 m = nThe line y =
a/c is a horizontal asymptote.
Case 3 m > nThe graph has no
horizontal asymptote.
y = axm
cxn ___
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5.3 Graphing General Rational Functions.notebook May 11, 2015
Example 3: Find all the vertical and horizontal asymptotes.
2x2 2x + 1 x2 x 12f(x) =
vertical:
horizontal:
HolesIf x b is a factor of both the numerator and
denominator then there is a hole in the graph when x = b unless it is a vertical asymptote.
3x2 + x3 x2 + 2x 3
f(x) =
HA:
VA:
Hole:
Example 4: Identify all the asymptotes and holes
in the graph.
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5.3 Graphing General Rational Functions.notebook May 11, 2015
Graph the function.1. Find all the xintercepts, asymptotes and holes, and graph them. 2. Use the graphing calculator tofind some more points.
2x 1
x + 4y =Example 5
xintercept(s):
Vertical Asymptote:
Horizontal Asymptote:
Holes:
D:
R:
y = 3x 28 + x2
x2 + 12x + 35
Example 6
xint:
VA:
HA:
Holes:
D:
R:
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5.3 Graphing General Rational Functions.notebook May 11, 2015
Example 7
xint:
VA:
HA:
Holes:
D:
R:
y = x2 +1 x2 1
Example 8
xint:
VA:
HA:
Holes:
D:
R:
y = 4x2 5x + 4 _________
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5.3 Graphing General Rational Functions.notebook May 11, 2015
Assignment: p. 322 # 8, 10, 12, 16, 22