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Home > PC > Chapter 5 > Lesson 5.1.3 > Problem 5-39

5-39.

The graphs of , , and , are shown above. Below are the graphs of the reciprocal of two of the functions from above. Express and in terms of one of the functions listed above.  

When , then is undefined, creating a vertical asymptote.

  1. Rational curve, with 4 sections separated by vertical asymptotes at x = negative 4, x = 1, &, x = 4, first section, opens up, above x axis. Second section, between the asymptotes, opening down with approximate turning point at (negative 2, comma negative 0.2). Third section, opening up with turning point at (2.5, comma 0.5). Right section, opening down, below the x axis.

  1. Rational curve, with 3 sections separated by vertical asymptotes at x = negative 1, &, at x = 3, left section, opens down, below x axis, Center section, opens up with turning point at (1, comma 1 fourth). Right section, opening down, below the x axis.

  1. Sketch the reciprocal of the function that was not used in parts (a) or (b).