samanthasnyder90 samanthasnyder90
  • 02-11-2018
  • Mathematics
contestada

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

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PiaDeveau PiaDeveau
  • 11-11-2018

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 = [tex]\frac{(x+1)(x-1)}{(x-2)(x+5)}[/tex].

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

Multiplying above express by 9 on the top, we get

[tex]f(x)=\frac{9(x+1)(x-1)}{(x-2)(x+5)}[/tex].

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

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