Question

follow the seven step strategy to graph the following rational function.
$f(x) = \frac{3x}{x^2 - 4}$
what is the y-intercept? select the correct choice below and, if necessary, fill in the answer box to complete your
a. the y-intercept is 0.
(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 comp choice.
a. the x-intercept(s) is
(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 of a function \(y = f(x)\) is the value of \(x\) when \(y=0\) (i.e., \(f(x) = 0\)). For the rational function \(f(x)=\frac{3x}{x^{2}-4}\), we set \(f(x) = 0\).

Step2: Solve for x when f(x)=0

Set \(\frac{3x}{x^{2}-4}=0\). A fraction is equal to zero when its numerator is zero (and the denominator is not zero at that \(x\)-value). So we solve \(3x = 0\). Dividing both sides by 3, we get \(x = 0\). Now we check the denominator at \(x = 0\): \(x^{2}-4=0^{2}-4=- 4
eq0\). So \(x = 0\) is a valid solution.

Answer:

A. The x - intercept(s) is \(0\)