Guide to graphing rational functions
Friday, April 18, 2025
11:00 AM
1. Notice power of numerator and denominator
The power of numerator and denominator are equal:
HORIZONTAL ASYMPTOTE
The numerator is one power greater
than the denominator:
SLANT ASYMPTOTE (instead of HA)
2. Factor if possible:
2. Factor if possible:
*NOTICE: Is there a common factor on top and bottom?
No common factor so no hole
3. X-intercept:
3. If there is a common factor, we get a HOLE
4. Y-intercept:
• We use this version of f(x) moving forward
5. Vertical asymptote:
The x-coordinate of the hole is the value of x that makes the
canceled factor equal 0. So in this case, x-1=0 at x=1
6. Slant asymptote: polynomial division
4. Find x-intercepts:
To find the x-intercepts, set the NUMERATOR=0
5. Y-intercept:
6. Vertical asymptote:
Plug in x=0:
6. Vertical asymptote:
Set denominator = 0
7. Horizontal asymptote:
Take lim as x goes to infinity of f(x):
8. Graph and label with key features: