Question

PLEASE ANSWER ASAP!!Find a rational function that might have the given graph. (More than one answer might be possible.)

Answer 1

The rational function that might have the given graph is
`y = - (x)/((x+1)\cdot (x-1) )`.

Explanation:

This graph shows a rational function whose numerator is a first order polynomial and denominator is a second order, due to the presence of vertical asymptotes at
`x = -1` and
`x = 1`. The lead coefficient of the numerator must be 1, since horizontal asymptote must be
`y = 0` and intercept must be
`0`, since
`y(0) = 0`.

Then, we conclude that a rational function that might have the graph is:

`y = - (x)/((x+1)\cdot (x-1) )` (1)

We present the proof that given function is appropriate.