Question

follow the seven step strategy to graph the following rational function.
$f(x) = \frac{3x}{x^2 - 4}$

to graph the function, first determine the symmetry of the graph of $f$. choose the correct answer below.
\bigcirc \\ y-axis symmetry
\bigcirc \\ neither y-axis symmetry nor origin symmetry
\bigcirc \\ origin symmetry

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

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \(y = f(x)\) is the value of \(y\) when \(x = 0\), provided that \(x = 0\) is in the domain of the function.

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

Given \(f(x)=\frac{3x}{x^{2}-4}\), substitute \(x = 0\) into the function:
\(f(0)=\frac{3\times0}{0^{2}-4}=\frac{0}{- 4}=0\)

Since \(x = 0\) is in the domain of the function (the denominator \(0^{2}-4=-4
eq0\) when \(x = 0\)), the y - intercept exists and is \(0\).

Answer:

A. The y - intercept is \(0\)