1. Honors Precalculus October 12-14, 2016 Mrs. Agnew
Rational Functions
Honors Precalculus
October 12-14, 2016
Mrs. Agnew

2. Essential Question Essential Vocabulary
How do you graph rational functions?
Essential Vocabulary
Rational Function
Asymptote (vertical, horizontal, slant)
Hole
Intercepts

3. Graphs of Rational Functions
The parent function of rational functions is y = 1/x
What are some of the distinguishing characteristics of this graph?
Prior to graphing any rational function, it is important to examine the domain of the rational function. (Remember: denominator ≠ 0)

4. Asymptotes Three types of asymptotes: Vertical Asymptote
Horizontal Asymptote
Slant/Oblique Asymptote
Occur when degree of numerator is exactly one more than degree of denominator

5. Vertical Asymptote
The graph of a function NEVER crosses a vertical asymptote.
The y-values go towards ∞ or -∞ at a vertical asymptote.
Vertical asymptotes occur where denominator equals zero.
Check for holes first…

6. Holes in the Graph
Hole in graph when common factor on top and bottom of fraction.
Cancel the common factor and then plug in “bad” x-value to find hole. (Remember: a hole must have an x- and a y-coordinate.)

7. Horizontal Asymptote Horizontal asymptote is line where graph
“levels off” as the x values go towards ∞ or -∞.
Horizontal Asymptote Theorem
Bigger exponent on top, no HA
Bigger exponent on bottom, HA y = 0.
If exponent same top and bottom, HA is equal to ratio of leading coefficients.
Examples…

8. Slant Asymptote
Slant asymptotes occur when degree of numerator is exactly one more than degree of denominator.
Use long division to find slant asymptote. The quotient (without the remainder) is the SA.
Examples…

9. Homework:
Page 225
#14-24 even, 43, 44, 49, 50, 51, 54

10. Graphing Rational Functions
Steps in graphing rational functions
Identify horizontal/slant asymptotes (if any)
Factor completely
Identify holes (if any)
Identify vertical asymptotes (if any)
Identify intercepts
Find test points and graph
Examples: page 234 #8 – 44 (Even), 46, 50, 54

11. Homework:
Worksheet Provided