Question

the graph of the function $f(x)$ is shown below. state all values of $x$ in the open interval $-9 < x < 9$ for which the function has a jump discontinuity.
answer attempt 1 out of 4
additional solution no solution

Explanation:

Step1: Recall the definition of jump discontinuity

A jump discontinuity occurs at a point \(x = a\) if \(\lim_{x
ightarrow a^{-}}f(x)\) and \(\lim_{x
ightarrow a^{+}}f(x)\) both exist, but \(\lim_{x
ightarrow a^{-}}f(x)
eq\lim_{x
ightarrow a^{+}}f(x)\)

Step2: Analyze the graph

By observing the graph of the function \(y = f(x)\) in the interval \(-9\lt x\lt9\), we look for points where the left - hand limit and the right - hand limit of the function are different.

We can see that at \(x=-3\), the left - hand limit (approaching from the left side of \(x =-3\)) and the right - hand limit (approaching from the right side of \(x=-3\)) of the function \(f(x)\) are different.

Answer:

\(x=-3\)