Write an equation for a rational function with Vertical asym

Write an equation for a rational function with: Vertical asymptotes of x = - 6 and x = 3 x intercepts of (4, 0) and (-3, 0) Horizontal asymptote of y = 5 Use y as your output variable. _____________________________

Solution

vertical asymptote x = -6 and x = 3

x intercepts 4 , -3

horizontal asymptote y = 5

y = ( x - 4 ) ( x + 3 ) / ( x + 6 ) ( x - 3 )

y = 5 ( x- 4 ) ( x +3 ) / ( x+ 6 ) ( x- 3 )

y = 5 (x^2 - x -12 ) / (x^2 + 3x - 18 )

therefore function is

y = ( 5x^2 - 5x - 60 ) / (x^2 + 3x - 18 )