Rational function equation

Question

Write an equation for a rational function with:

Vertical asymptotes at x = -2 and x = -1

x intercepts at x = 5 and x = 4

Horizontal asymptote at y = 9

y =

Answer 1

Vertical asymptote occur when denominator is set to 0. Horizontal asymptote can be found when the degree of the denominator equals the degree of the numerator and then it is the ratio of the coefficients of numerator to denominator of the highest degree terms. X intercepts occur when y equals 0. 

 

The info given concludes that this is a 2nd degree polynomial for both numerator and denominator. 

 

Y=9[(X-5)(x-4)]/[(x--2)(X--1)]

 

this simplifies to 

 

y=(9x² -81x+180)/(x² +3x+2)