2.7 Graphs of Rational Functions

Steps of Graphing

1. Find the domain of the function

2. Simplify the function

3. Find and plot the y-intercept by evaluating f(0)

4. Find and plot the x-intercept by solving N(x) = 0

5. Find and graph the vertical asymptotes by solving D(x) = 0

6. Find and graph the horizontal asymptotes by comparing the degrees

7. If no HA, find and graph the slant asymptote by dividing N(x)/D(x)

8. Find additional points in between each x-int and VA

9. Draw smooth curves to complete the graph

Graph

Graph

Graph

Graph

1.

2.

HomeworkPg 157-158 #15, 21, 23, 47, 50

WAC Type 3

FCA1: Compare and contrast vertical asymptotes and holes in rational functions. (2pts)

FCA2: Compare and contrast horizontal asymptotes and slant asymptotes in rational functions. (2pts)

FCA3: All answers must be written in complete sentences. (2pts)

Graph

Graph

Graph

Find the range