1. Graphing Rational Functions

2. To Graph Rational Functions
Horizontal Asymptotes: compare the
degrees of the numerator and denominator.

3. Horizontal Asymptote If then HA: y = 0 If then HA: y = 2 If HA: none
you look at
then
HA: y = 2 If
then there is NO horizontal asymptote
HA: none

4. To Graph Rational Functions
2. Find the y-intercept: x equal to zero. Solve for y.
Factor Completely
4. Holes:
Look at factors that are common to numerator
and denominator. Set those equal to 0 and solve.
Substitute back into new equation.

5. To Graph Rational Functions
5. Vertical Asymptotes: set the denominator
equal to zero. It is stated as an equation.
The vertical asymptotes do not include the holes
6. Roots: set the numerator = 0 and solve.
these are also called the x-intercepts and zeros

6. Example 1 Example 2 Identify the following for
Horizontal asymptote Vertical Asymptote
Y-intercept:
Roots:
Holes: 6

7. Example 2 none Identify the following for
Horizontal asymptote Vertical Asymptote
Y-intercept: Roots:
Holes:
Look at the degrees
none
2/16/ :03 PM 7

8. Example 3 Identify the following for Horizontal Asymptote Holes
look at the degrees
Vertical asymptote
y-intercept
Roots 8 8

9. Example 4 Identify the following for Horizontal Asymptote Holes
look at the degrees
Vertical asymptote
Roots
y-intercept
2/16/ :03 PM 9 9

10. Example 5 Identify the following for Horizontal Asymptote Holes
look at the degrees
Vertical asymptote
y-intercept
Roots 10 10

11. Example 6 Identify the following for Horizontal Asymptote Holes
look at the degrees
Vertical asymptote
y-intercept
Roots 11 11

12. Example 7 Identify the following for Horizontal Asymptote Holes
look at the degrees
Vertical asymptote
y-intercept
Roots 12 12