Find an algebraic representation of a rational function f wi

Find an algebraic representation of a rational function f with the following properties, f has a vertical asymptote of x = -2, a hole at x = 4, x-intercept (-1, 0), and end behavior model of q(x) = -x + 5.

Solution

vertical asymtote at (x= -2) = 1/(x+2)

When a value of x sets both the denominator and the numerator of a rational function equal to 0, there is a hole in the graph.Hole x= 4

f(x) = (x-4)/(x+2)(x-4)

x intercept : (-1 , 0)

f(x) = (x+1)(x-4)/(x+2)(x-4) = (x^2 -3x +4)/(x^2 -2x -8)