Question

use the graph to answer the question. which correctly describes the point of discontinuity of the function? (1 point) there is a jump discontinuity at $x = -3$. there is a removable discontinuity at $x = 1$. there is a jump discontinuity at $x = 1$. there is a removable discontinuity at $x = -3$.

Explanation:

Step1: Recall definitions

A jump discontinuity occurs when the left - hand limit and the right - hand limit of a function at a point \(x = a\) exist but are not equal. A removable discontinuity occurs when the left - hand limit and the right - hand limit of a function at a point \(x = a\) exist and are equal, but the function is not defined at \(x = a\) or the function value at \(x = a\) is not equal to the limit.

Step2: Analyze the graph at \(x=-3\)

Looking at the graph, as \(x\) approaches \(-3\) from the left, the function has one value (a horizontal line approaching a certain \(y\) - value), and as \(x\) approaches \(-3\) from the right, the function has a different \(y\) - value. The left - hand limit and the right - hand limit exist but are not equal.

Step3: Analyze the graph at \(x = 1\)

The graph is continuous at \(x = 1\). There is no break, hole, or jump at \(x=1\).

Answer:

There is a jump discontinuity at \(x=-3\)