Below is the graph of a rational function Determine the foll

Below is the graph of a rational function. Determine the following: Solve f(x) = 0 The equations of the vertical asymptotes. The equation of the horizontal asymptote Write the factored rational function f(x) = (x-c_1)(x - c_2)/(x - c_3)(x - c_4)

Solution

a) f(x) = 0

From the graph ==> x = -1 , x = 1

b) Equations of vertical asymptote

==> x = -2 , x = 2

since at x = -2 , x = 2 function is undefined.

c) equation of horizontal asymptote

==> y = 1/4

since as x is very large the value of f(x) tending to 1/4

d) Hence f(x) = (x - 1)(x + 1) / [(x + 2)(x - 2)]