1. Table of Contents Rational Functions: Sketching Graphs Example: Sketch the graph of, First find the intercepts. To find the x-intercept(s), set f (x) = 0 and solve. 3x + 5 = 0,3x = - 5,x = - 5/3,x-intercept: (- 5/3, 0) To find the y-intercept(s), set x = 0 and solve. y-intercept: (0, - 5/2)

2. Table of Contents Rational Functions: Sketching Graphs Slide 2 Example: Sketch the graph of, (continued) Second, find the asymptotes. To find the vertical asymptote(s), set the denominator equal to 0 and solve. x – 2 = 0, vertical asymptote: x = 2 Since the degrees of the numerator and denominator are the same (see separate slideshow), the horizontal asymptote is: y = 3/1. horizontal asymptote: y = 3 Third, plot the intercepts and asymptotes found on the rectangular coordinate plane (click to see on next slide).

3. Table of Contents Rational Functions: Sketching Graphs Slide 3 7 7 - 7 x-intercept: (- 5/3, 0) y-intercept: (0, - 5/2) vertical asymptote: x = 2 horizontal asymptote: y = 3 Example: Sketch the graph of, (continued)

4. Table of Contents Rational Functions: Sketching Graphs Slide 4 Example: Sketch the graph of, (continued) Fourth, graph the function in the standard viewing window by pressing, entering the function, and pressing. Y = ZOOM 6 NOTES: (2) There is a solid vertical line where the vertical asymptote is located. (3) The horizontal asymptote is not shown. (1) The intercepts check . (4) The graph is in two separate parts.

5. Table of Contents Rational Functions: Sketching Graphs Slide 5 Example: Sketch the graph of, (continued) 7 7 - 7 Fifth, graph the parts shown by the graphing calculator. Also, it is good to show one point that the graph passes through in each region. (5, 20/3) Take care to see that the graph passes through the intercepts.

6. Table of Contents Rational Functions: Sketching Graphs Slide 6 Try: Sketch the graph of, 7 7 - 7 (3, 13/5) V.A. x = 2V.A. x = - 2 H.A. y = 1 (- 3, 13/5) y-int. (0, - 1)

7. Table of Contents Rational Functions: Sketching Graphs