1. Rational Functions II: Analyzing Graphs
Objectives:
Analyze the Graph of a Rational Function
Solve Applied Problems involving Rational Functions

2. Analyzing the Graph of a Rational Function
1. Find the domain of the Rational Function
2. Locate the intercepts, if any, of the graph. The x-intercepts, if any, are numbers in the domain that satisfy the equation The y-intercept, if there is one, is
3. Test for symmetry. Replace If there is symmetry with respect to the y-axis. If there is symmetry with respect to the origin.
4. Write in lowest terms and find the real zeros of the denominator. With in lowest term, each zero will give rise to a vertical asymptote.
5. Locate the horizontal or oblique asymptotes, if any, using the procedure given earlier. Determine points, if any, at which the graph of intersects these asymptotes.
6. Determine where the graph is above the x-axis and where the graph is below the x-axis using the zeros of the numerator and the denominator to divide the x-axis into intervals.
7. Graph the asymptotes, if any, found in steps 4 and 5. Plot the points found in steps 2,5 and 6. Use all the information to connect the points and graph

3. EX: Graph the rational function1.

4. EX: Graph the rational function2.

5. EX: Graph the rational function3.

6. EX: Graph the rational equation4.