1. 11.2 – Graphing Rational Functions
Definitions of the Day (DODs)
Rational Function
Asymptote

2. Examples: Definition: Rational Function:
A function that can be written in the form
Examples:

3. Definition: A line is an asymptote of a graph if the graph of the function gets closer and closer to the line, but does not cross it.
Example:
The red lines are asymptotes.
One line is a vertical asymptote (x = 0).
The other line is a horizontal asymptote (y = 0).
Notice that the graph approaches the asymptotes, but does not cross them.

4. Evaluate each rational function for x = 3.
Finding Vertical Asymptotes
Evaluate each rational function for x = 3.

5. To find vertical asymptotes, we will set the denominator equal to zero and solve for x.
Find the vertical asymptote for each rational function.

6. Steps to graphing a rational function:
1. Find the vertical asymptote. The vertical asymptote is where the denominator equals zero.
2. Make a table of values around the asymptote.
3. Draw the graph (remember to show the asymptote by using a dashed line).

7. Graphing a rational function
Graph the function

8. Graphing a rational function
Graph the function

9. Your Turn!! Evaluate the rational function for x = -2
Graph the following function

10. Sentence Frames A rational function is a __________ over another
___________.
To find a vertical asymptote, I need to _________________________________________.