1Areciprocalwksolns

Reciprocal Graphs: Worksheet


 * Solutions **

a) Reciprocal of y = 2x + 2



Domain: x Î **R**\{–1} Range: y Î **R**\{0}

Asymptotes: x = –1, y = 0 y-intercept: y = 0.5

b) Reciprocal of y = x 2 + 1



Domain: x Î **R** Range: y Î (0, 1]
 * {Notice the top of the red curve is smooth -- not a point!} **

Asymptotes: y = 0 Stationary Points: Local maximum at (0, 1) y-intercept: y = 1

c) Reciprocal of y = –(x – 2) 2 + 2



math \textbf{Domain: } x \in R \backslash \{ 2-\sqrt{2}, \; 2+\sqrt{2} \} math Range: y Î (– ¥, 0) È [0.5, + ¥ ) (or) Range: y Î **R** \ [0, 0.5)

math \textbf{Asymptotes: } y=0, \; x=2-\sqrt{2}, \; x=2+\sqrt{2} math

Stationary Point: Local minimum at (2, 0.5)

y-intercept: y = –0.5

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