Math Problem Statement
Solution
The graph provided shows , and we are tasked with determining where is continuous. A function is continuous if there are no breaks, jumps, or holes in the graph.
Observations from the Graph:
-
There are visible discontinuities:
- At : A jump discontinuity.
- At : A hole (removable discontinuity).
-
The function appears continuous elsewhere.
Continuity:
The function is continuous:
- On the intervals , , and .
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Related Questions:
- What are the different types of discontinuities in a graph?
- How do you test for continuity algebraically at a specific point?
- Why is a jump discontinuity different from a removable discontinuity?
- How can you modify to make it continuous everywhere?
- What real-world problems rely on continuous functions?
Tip: Always examine both the left-hand and right-hand limits to confirm continuity at a point.
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Math Problem Analysis
Mathematical Concepts
Graph Analysis
Continuity of Functions
Types of Discontinuities
Formulas
N/A (graph-based analysis)
Theorems
Definition of Continuity
Intermediate Value Theorem
Suitable Grade Level
Grades 11-12
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