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