1 Analyze and sketch graphs of rational functions. 2.6 What You Should Learn

2 Analyzing Graphs of Rational Functions

3 To sketch the graph of a rational function, use the following guidelines.

4 Analyzing Graphs of Rational Functions You may also want to test for symmetry when graphing rational functions, especially for simple rational functions. Recall that the graph of f (x) = 1/x is symmetric with respect to the origin.

5 Example 1 – Sketching the Graph of a Rational Function Sketch the graph of and state its domain. Solution: y-intercept: because g(0) = x-intercept: None, because 3 ≠ 0 Vertical asymptote: x = 2, zero of denominator Horizontal asymptote: y = 0, because degree of N(x) < degree of D(x)

6 Example 1 – Solution Additional points: By plotting the intercepts, asymptotes, and a few additional points, you can obtain the graph shown in Figure 4.8. The domain of g is all real numbers except x = 2. cont’d Figure 4.8

7 Analyzing Graphs of Rational Functions The graph of g in Example 1 is a vertical stretch and a right shift of the graph of because