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.

Explanation:

Step1: Recall jump - discontinuity definition

A function $y = f(x)$ has a jump discontinuity at $x = a$ 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: Examine the graph

By looking at the graph of $y = f(x)$ in the open - interval $-9\lt x\lt9$, we can see that at $x=-7$, the left - hand limit $\lim_{x
ightarrow - 7^{-}}f(x)$ and the right - hand limit $\lim_{x
ightarrow - 7^{+}}f(x)$ both exist and are not equal. Also, at $x = 2$, the left - hand limit $\lim_{x
ightarrow 2^{-}}f(x)$ and the right - hand limit $\lim_{x
ightarrow 2^{+}}f(x)$ both exist and are not equal.

Answer:

$x=-7, x = 2$