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:
- The graph has a break (discontinuity) at . At this point, the graph has a hole, and then it continues from a different value. This indicates a jump discontinuity.
- There is no apparent discontinuity at . The graph seems continuous at this point.
Conclusion:
The correct answer is:
- c. there is a jump discontinuity at
Would you like more details or have any further questions?
Here are some related questions to consider:
- What is the difference between a jump discontinuity and a removable discontinuity?
- How can you algebraically identify the location of a discontinuity in a function?
- What types of functions typically exhibit jump discontinuities?
- How does a removable discontinuity differ from an asymptote?
- 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.
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Math Problem Analysis
Mathematical Concepts
Functions
Discontinuities
Graphical analysis
Formulas
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Theorems
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Suitable Grade Level
High School
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