Question

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

Answer 1

Answer:

The rational function that might have the given graph is $y = - \frac{x}{(x+1)\cdot (x-1) }$.

Step-by-step 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:

$y = - \frac{x}{(x+1)\cdot (x-1) }$ (1)

We present the proof that given function is appropriate.