Given the following information about a rational function de

Given the following information about a rational function, determine its equation. The zero of the function is x = 4, the y-intercept is -2, the equations of the asymptotes are x = 2 and y = -1. 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. 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.

Solution

5)   zero x = 4

y intercept =- 2

equation of asymptotes

x = 2 , y = -1

zero come in the numerator and vertical asymptotes in denominator

therefore, function becomes

f(x) = -1(x-4) / (x-2)

6) zero = x = -1 , y intercept = 2

asymptotes

x =-2, x = 3 , y= 0

zero come in the numerator and vertical asymptotes in denominator

since horizontal asymptote is y =0 degree of denominator would be greater

so let function be

f(x) = a(x+1) / (x+2)(x-3)

plugging (0,2) point in the function and solving for a

2 = a(0+1) / (0+2)(0-3)

a = -12

hence, function is f(x) = -12 (x+1) / (x+2)(x-3)