Question

Write an equation for a rational function with: vertical asymptotes at x = 2 and x = -5 x-intercepts (-1,0) and (1,0) horizontal asymptote at y = 9

Answer 1

Given vertical asymptotes x = 2 and x = -5 .

Therefore Factors of denominator (x-2)(x+5).

x-intercepts (-1,0) and (1,0) .

Therefore factors of (x+1)(x-1).

So far we got rational function = $\frac{(x+1)(x-1)}{(x-2)(x+5)}$.

Now, we are given horizontal asymptote at y = 9.

Multiplying above express by 9 on the top, we get

$f(x)=\frac{9(x+1)(x-1)}{(x-2)(x+5)}$.

Therefore, required rational function is $f(x)=\frac{9(x+1)(x-1)}{(x-2)(x+5)}$.