Question

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

to graph the function, first determine the symmetry of the graph of f. choose the correct answer below.

• neither y - axis symmetry nor origin symmetry
• y - axis symmetry
• origin symmetry

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 \boxed{}.
( type an integer or a simplified fraction. )
b. there is no y - intercept.

Explanation:

Step1: Recall y-intercept definition

The y-intercept of a function \( f(x) \) is the value of \( f(0) \), found by substituting \( x = 0 \) into the function.

Step2: Substitute \( x = 0 \) into \( f(x) \)

Given \( f(x)=-\frac{2}{x^{2}-9} \), substitute \( x = 0 \):
\( f(0)=-\frac{2}{0^{2}-9}=-\frac{2}{-9}=\frac{2}{9} \).

Answer:

A. The y-intercept is \(\frac{2}{9}\)