Math Problem Statement

Use the graph to answer the question.

Which correctly describes the point of discontinuity of the function?

a. there is a jump discontinuity at x=-3 b. there is a removable discontinuity at x=1 c. there is a jump discontinuity at x=1 d. there is a removable discontinuity at x=-3

Solution

To determine the correct description of the point of discontinuity from the graph, let's analyze the provided image.

Observations from the Graph:

  1. The graph has a break (discontinuity) at x=1x = 1. At this point, the graph has a hole, and then it continues from a different value. This indicates a jump discontinuity.
  2. There is no apparent discontinuity at x=3x = -3. The graph seems continuous at this point.

Conclusion:

The correct answer is:

  • c. there is a jump discontinuity at x=1x = 1

Would you like more details or have any further questions?

Here are some related questions to consider:

  1. What is the difference between a jump discontinuity and a removable discontinuity?
  2. How can you algebraically identify the location of a discontinuity in a function?
  3. What types of functions typically exhibit jump discontinuities?
  4. How does a removable discontinuity differ from an asymptote?
  5. How can discontinuities affect the derivative of a function?

Tip: When dealing with graphs, carefully examine the behavior of the function at specific points to identify different types of discontinuities.