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Worksheet – 3.7 NAME________________________________ Give exact answers for parts (a) – (g) for the following 4 functions. Be sure to support your answers. (a) Determine the equation of any horizontal or slant asymptote. (b) Determine the equation(s) of any vertical asymptote(s). (c) Give the y-intercept. (d) Calculate the zeros of the function. (e) When the input approaches infinity, is the function above or below the horizontal asymptote? (f) When the input approaches negative infinity, is the function above or below the horizontal asymptote? (g) Without using a calculator, neatly graph the function showing each asymptote with a dotted line. 1. f ( x) 2. g (t ) 3. h( w) 2 x 2 x 15 x 2 2x 3 t 8 t 16 2 w 3 w 2 6w w2 1 4. k ( x) 3x 2 13x 4 x 2 x 20 Given the following information about a rational function, determine its equation. 5. The zero of the function is x = 4, the y-intercept is –2, the equations of the asymptotes are x = 2 and y = -1. 6. The zero of the function is x = -1, the y-intercept is 2, the equations of the asymptotes are x = -2, x = 3, and y = 0. 7. The zeros of the function are x = -1.5 and x = 2, the y-intercept is 3, the equations of the asymptotes are x = -2, x = 1, and y = 2.