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Rational Functions: Sketching Graphs

Example: Sketch the graph of,. Rational Functions: Sketching Graphs . 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.

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Rational Functions: Sketching Graphs

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  1. Example: Sketch the graph of, Rational Functions: Sketching Graphs 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. Example: Sketch the graph of, (continued) Rational Functions: Sketching Graphs Second, find the asymptotes. To find the vertical asymptote(s), set the denominator equal to 0 and solve. vertical asymptote: x = 2 x – 2 = 0, 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). Slide 2

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

  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 (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. Rational Functions: Sketching Graphs NOTES: Slide 4

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

  6. 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 Rational Functions: Sketching Graphs Slide 6

  7. Rational Functions: Sketching Graphs END OF PRESENTATION Click to rerun the slideshow.

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