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2.7 Graphs of Rational Functions. Steps of Graphing. Find the domain of the function Simplify the function Find and plot the y-intercept by evaluating f(0) Find and plot the x-intercept by solving N(x) = 0 Find and graph the vertical asymptotes by solving D(x) = 0 - PowerPoint PPT Presentation
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2.7 GRAPHS OF RATIONAL
FUNCTIONS
STEPS OF GRAPHINGFind the domain of the function
Simplify the function
Find and plot the y-intercept by evaluating f(0)
Find and plot the x-intercept by solving N(x) = 0
Find and graph the vertical asymptotes by solving D(x) = 0
Find and graph the horizontal asymptotes by comparing the degrees
Find additional points
Draw smooth curves to complete the graph
GRAPH
23)(
x
xf
GRAPH
xxxf 12)(
GRAPH
2)( 2
xxxxf
GRAPH
329)( 2
2
xx
xxf
SLANT ASYMPTOTES
If the degree in the numerator is exactly one more than the degree in the denominator, then a slant asymptote exists.
To find the equation for the slant asymptote• Using synthetic or long division divide• The equation is the quotient without the
remainder
GR APHIN G WITH SL ANT ASY MPTOTES
12)(
2
xxxxf
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