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) =

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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)

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).

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

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.

Table of Contents Rational Functions: Sketching Graphs Slide 5 Example: Sketch the graph of, (continued) 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.

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

Table of Contents Rational Functions: Sketching Graphs