Question

homework: practice what you missed final exam part b question part 5 of 9 the function f(x) = \\(\frac{1}{x^2 - 9}\\) is a rational function. answer parts (a) - (i). d. find the y-intercept or state that the function does not have a y-intercept. select the correct choice and a. the y-intercept is y = \\( -\frac{1}{9} \\). (simplify your answer. type an integer or a simplified fraction.) b. the function has no y-intercept. e. find all x-intercepts or state that the function has no x-intercepts. select the correct choice and, if nece a. the x-intercept(s) is(are) x = . (simplify your answer. type an integer or a simplified fraction. use a comma to separate answers b. the function has 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., we need to solve \(f(x)=0\) for \(x\).
Given \(f(x)=\frac{1}{x^{2}-9}\), set \(f(x) = 0\), so we have the equation \(\frac{1}{x^{2}-9}=0\).

Step2: Analyze the equation

For a fraction \(\frac{a}{b}\) to be equal to \(0\), the numerator \(a\) must be \(0\) and the denominator \(b
eq0\). In the equation \(\frac{1}{x^{2}-9}=0\), the numerator is \(1\), which is never equal to \(0\). So, there is no solution for \(x\) when \(f(x) = 0\).

Answer:

B. The function has no x - intercept.