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Lesson 2.6 Rational Functions and Asymptotes. Graph the function: Domain: Range: Increasing/Decreasing: Line that creates a split in the graph:. Rational Functions Where N(x) and D(x) are polynomials Discontinuities: places where the graph “skips” or “jumps” - PowerPoint PPT Presentation
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Lesson 2.6Rational Functions and
Asymptotes
Graph the function:
Domain:
Range:
Increasing/Decreasing:
Line that creates a split in the graph:
1
1
x
xxf
Rational Functions
Where N(x) and D(x) are polynomials
Discontinuities: places where the graph “skips” or “jumps”
Graph and look for discontinuities:
)(
)(
xD
xNxf
1
12
x
xxf
4
82 2
x
xxxf
1
1
x
xxf
Discontinuities
Hole: can be factored out
Jumps: cannot be factored out
Asymptotes (jumps)
A horizontal or vertical line through which a graph is undefined
Cannot be factored out
Finding location of asymptotes:
Given ; n = degree of N(x), d = degree of D(x)
Vertical asymptote(s): At zeros of D(x); Write “x = #”
Horizontal asymptote(s):
If n < d → → y = 0
If n = d → →
If n > d → → no horizontal asymptote
)(
)(
xD
xNxf
1
12
x
x
1
523
3
x
x
8
3
xx
xDoftcoefficienleading
xNoftcoefficienleadingy
___
___
Example
Find all discontinuities of 6
22
2
xx
xxxf
Problem Set 2.6