1. Graphs of Rational Functions
Section 2.7
Graphs of Rational Functions

2. Objective By following instructions students will be able to:
Analyze and sketch graphs of rational functions.
Decide whether graphs of rational functions have slant asymptotes.
Use rational functions to model and solve real-life problems.

3. Rational Functions Vertical asymptote x=0
Vertical asymptotes: “certain” asymptote
D(x)=0
(solve for the variable)
Horizontal asymptote
y=0

4. Rational Functions
Horizontal asymptotes “uncertain” asymptote (determined by degree) n=degree of N(x) d=degree of D(x)
Less Than
Equal to
Greater Than
n=d +1
no horizontal asymptote

5. Example 1:
Sketch the graph of .

6. Example 2:
Graph . Identify the domain and the range.

7. Example 3:
Graph

8. U-TRY #1
Graph. 1) 2)

9. Example 4:
Graph

10. Slant Asymptotes
If numerator = denominator +1, then the function has a slant asymptote.
Ex.
Using, long division.
x-2 is the slant asymptote

11. Example 5:
Graph

12. Example 6:
A rectangular page is designed to contain 48 square inches of print. The margins of each side of the page are each 1 ½ inches. The margins at the top and bottom are each 1 inch. What should the dimensions of the page be so that the minimum amount of paper is used?

13. Revisit Objective Did we…
Analyze and sketch graphs of rational functions?
Decide whether graphs of rational functions have slant asymptotes?
Use rational functions to model and solve real-life problems?

14. Homework
Pg 204 #s 1-69 EOO