Question

follow the seven step strategy to graph the following rational function.
$f(x) = -\frac{2}{x^2 - 9}$

what is the y-intercept? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the y-intercept is $\frac{2}{9}$.
(type an integer or a simplified fraction.)
b. there is no y-intercept.

what is/are the x-intercept(s)? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the x-intercept(s) is/are .
(type an integer or a simplified fraction. use a comma to separate answers as needed.)
b. there is no x-intercept.

Explanation:

Step1: Recall x-intercept definition

The x-intercept occurs where \( f(x) = 0 \). So we set \( -\frac{2}{x^2 - 9} = 0 \).

Step2: Solve for x

For a fraction \( \frac{a}{b} = 0 \), the numerator \( a \) must be 0 (and denominator \( b
eq 0 \)). Here, the numerator is \( -2 \), which is never 0. So there's no solution for \( x \) that makes \( f(x) = 0 \).

Answer:

B. There is no x - intercept.