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 an infinite discontinuity.

Explanation:

Step1: Recall infinite discontinuity

An infinite discontinuity occurs where the function has a vertical asymptote, meaning the function approaches \( \pm\infty \) as \( x \) approaches a value. From the graph, we look for \( x \)-values where the function's graph has a vertical asymptote (or behavior indicating unboundedness).

Step2: Identify \( x \)-values

Looking at the graph, at \( x = -3 \), the function has a vertical asymptote (the graph behaves as if it goes to \( \pm\infty \) near \( x = -3 \))? Wait, no, re - examining: Wait, the graph's behavior: Wait, the open circles and the asymptote - like behavior. Wait, actually, from the graph, the vertical asymptote (infinite discontinuity) occurs at \( x=-3 \)? Wait, no, let's check the graph again. Wait, the graph: looking at the \( x \)-axis, the points where the function has infinite discontinuity (vertical asymptote) are at \( x = - 3 \)? Wait, no, maybe I misread. Wait, the graph: the middle part, when \( x=-3 \), the function has a vertical asymptote? Wait, no, let's see the graph's structure. Wait, the problem is to find \( x \) in \( - 9

Answer:

\( x=-3 \)