Rational Functions Sketching Graphs Example Sketch the graph

Rational Functions: Sketching Graphs Example: Sketch the graph of, (continued) x-intercept: (- 5/3, 0)

Rational Functions: Sketching Graphs Example: Sketch the graph of, (continued) Fourth, graph the function

Rational Functions: Sketching Graphs Example: Sketch the graph of, (continued) Fifth, graph the parts

Rational Functions: Sketching Graphs Try: Sketch the graph of, 7 (3, 13/5) (- 3,

Rational Functions: Sketching Graphs Table of Contents

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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. 3 x + 5 = 0, 3 x = - 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 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 Slide 2

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

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

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

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

Rational Functions: Sketching Graphs Table of Contents