Question

Write the equation of a rational function that has vertical asymptote at x=-5 and x=0, a horizontal asymptote at y=4, x-intercepts at (-1,0) and (1,0), and no y-intercept.
Please help!

Answer 1

Rational Function...

vertical asymptote at x=-5 ==> \(y = \dfrac{1}{x+5}\)

vertical asymptote at x=0 ==> \(y = \dfrac{1}{x(x+5)}\)

Horizontal at y = 4 ==> \(y = \dfrac{4(x-2)^{2}}{x(x+5)}\) <== This was an arbitrary choice. The only WRONG numerator would be a factor of 'x' or 'x+5'

x-interecept at x = 1 ==> \(y = \dfrac{4(x-2)(x-1)}{x(x+5)}\)

x-interecept at x = -1 ==> \(y = \dfrac{4(x+1)(x-1)}{x(x+5)}\)

Just one piece at a time!

Answer 2

Thank you!

Answer 3

That was your one free one. Let's see you do one.