1. Today in Pre-Calculus Go over homework Notes: Homework
Graphs of rational functions
Homework

2. Graphs of Rational Functions
The line x = a is a vertical asymptote of the graph f(x) if
The line y = b is a horizontal asymptote of the graph of f(x) if,
vertical asymptote at x = 0
horizontal asymptote at y = 0

3. Graphical Features of Rational Functions
Vertical Asymptotes: occur at the zeros of the denominator provided they are not also zeros of the numerator of equal or greater multiplicity.
Horizontal Asymptotes: look at
If:
horizontal asymptote: y=0
horizontal asymptote: y=ratio of leading coefficients
no horizontal asymptote

4. Graphical Features of Rational Functions
Slant (or Oblique) Asymptotes: occur if the degree of numerator is exactly one more than the degree of denominator. Use polynomial long division, the quotient is the equation for the slant asymptote.
Note: Graphs NEVER intersect their vertical asymptotes but they can intersect slant and horizontal asymptotes.

5. Graphical Features of Rational Functions
X-intercepts: Occur when f(x) equals 0 (basically when the numerator equals 0, provided this is not also a zero of the denominator).
Y-intercepts: Occur at f(0), if defined.

6. Example 1 List the asymptotes and intercepts for the following graph.
Vertical asymptote: none
Horizontal asymptote: y=0
Slant asymptote: none
x-intercept: none
y-intercept: (0,4)

7. Example 2 List the asymptotes and intercepts for the following graph.
Vertical asymptote: x = –1
Horizontal asymptote: none
Slant asymptote: y = x – 2
x-intercept: (0,0),(1,0)
y-intercept: (0,0)

8. Example 3 List the asymptotes and intercepts for the following graph.
Vertical asymptote: x = –2 , 2
Horizontal asymptote: y=3
Slant asymptote: none
x-intercept: (0,0)
y-intercept: (0,0)

9. Homework
Pg. 245: 23-30all
Chapter 2 test: Tuesday, November 25