1. 3.5 Rational Functions II: Analyzing Graphs

2. Analyzing the Graph of a Rational Function
Find the domain of the rational function R.
Write R in the lowest terms.
Locate the x and y intercepts.
Test for symmetry.
Locate vertical asymptotes.
Locate horizontal and oblique asymptotes.
Graph R.

3. Analyze the graph of:

4. In lowest terms:
x-intercept: -1
y-intercept:
No symmetry

5. Vertical asymptote: x = -3
Hole: (3, 4/3)
Horizontal asymptote: y = 2

6. 1 -4 -2
R(1) = 1
R(-4) = 6
R(-2) = -2
Above x-axis
Above x-axis
Below x-axis
(-4, 6)
(-2, -2)
(1, 1)

7. x = - 3
(-4, 6)
(1, 1)
(3, 4/3)
y = 2
(-2, -2)
(-1, 0)
(0, 2/3)