Answer:
The rational function that might have the given graph is [tex]y = - \frac{x}{(x+1)\cdot (x-1) }[/tex].
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 [tex]x = -1[/tex] and [tex]x = 1[/tex]. The lead coefficient of the numerator must be 1, since horizontal asymptote must be [tex]y = 0[/tex] and intercept must be [tex]0[/tex], since [tex]y(0) = 0[/tex].
Then, we conclude that a rational function that might have the graph is:
[tex]y = - \frac{x}{(x+1)\cdot (x-1) }[/tex] (1)
We present the proof that given function is appropriate.
