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Consider a rational function

`f`

that satisfies the following conditions.

```
\lim_(x->+-\infty )f(x)=0,\lim_(x->0)f(x)=-\infty ,f(4)=0,
\lim_(x->8^(-))f(x)=\infty ,\lim_(x->8^(+))f(x)=-\infty ,
```

Find the factors of the denominator of

`f`

corresponding to the vertical asymptotes. (Enter your answers as a comma-separated list. Enter at least one expression for each vertical asymptote.) Find the factors of the numerator of

`f`

corresponding to the

`x`

-intercepts. (Enter your answers as a comma-separated list. Enter at least one expression for each

`x`

-intercept.) Which of the following must be true? The degree of the denominator is greater than the degree of the numerator. The degree of the numerator is greater than the degree of the denominator. The degrees of the numerator and the denominator are equal. Nicely done! Find an equation for

`f`

.

`f(x)=`

`◻`