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9.3 Intro to Rational Functions
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Transcript of 9.3 Intro to Rational Functions
9.3 Rational Functions and Their Graphs
A rational function is. . .
Examples of Rational Functions
Where does the denominator = 0?
Examples of Rational Functions
Where does the denominator = 0?
Examples of Rational Functions
Where does the denominator = 0?
A point of discontinuity occurs when. . .
It causes or
in the graph.
Example 1. Find the points of discontinuity.
a. 1x2x
1y
2 b.
1x
1xy
2
If a number is a solution to only the denominator of a rational function, then it creates an __________________ in the function.
ex.
)2x)(1x(
1xy
If a number is a solution to both the numerator and denominator of a rational function, then it creates a _____________ in the function.
ex.
)1x)(2x(
2xy
Example 2. Describe the vertical asymptotes and holes for the graph of each rational function.
a. b. )3x)(2x(
1xy
2x
)1x)(2x(y
c.
d.
)4x)(3x)(3x(
)4x)(3x(y
1x
1xy
2
Horizontal AsymptotesA horizontal asymptote depends on the
biggest power of the numerator and denominator.
1. If n > d,
2. If n < d,
3. If n = d,
Example 3. Find the horizontal asymptotes of each function.
a.
b.
c.
1x
6x2y
2x
1y
x5
x2xy
3
Example 4. Sketch the graph of
Points of discontinuity:
Holes:
Vertical Asymptotes:
Horizontal Asymptotes:
)4x)(3x(
2xy
Assignment:
