1. Rational Functions & Their Graphs1
Simplifying 2
Discontinuity, Intercepts & Asymptotes 3
Practice Problems

2. Rational Functions Rational Functions Continuous Functions
can be written as
Continuous Functions
can be graphed w/o lifting the pencil
are not undefined at any value
Discontinuous Functions
Can not be graphed w/o lifting the pencil
Are undefined at one or more values

3. Simplifying Steps COMPLETELY Factor the Numerator
COMPLETELY Factor the Denominator
Cancel Matching Factors/Terms

4. Simplifying Examples
Simplify

5. Discontinuity
Point of Discontinuity is any value that makes the function undefined (divide by zero)
Removable Discontinuity
Can be removed by Simplifying
Non-Removable Discontinuity
Can not be removed by simplifying

6. Discontinuity Example
What are the domain points of discontinuity? Are they removable or non-removable?
Discontinuous at x=3 and x=1
Non-removable

7. Horizontal Asymptotes
Horizontal asymptote at y=a/b where “a” is the coefficient of the term of the greatest power in the numerator and “b” is the coefficient of the term of the greatest power in the denominator.

8. Vertical Asymptotes
Non-removable points of discontinuity are vertical asymptotes !

9. Asymptote Example
What are the vertical asymptotes of

10. Another Asymptote Example
What are the horizontal asymptotes of
No Horizontal Asymptote

11. Intercepts Y-Intercept X-Intercept Set x=0 and solve (0, ?)
Set y=0 and solve
(?,0)

12. Intercept Example
Find the intercepts
Y-intercept
X-intercept