Math Problem Statement
Solution
To determine whether the graphed relation is a function or not, we use the Vertical Line Test:
- A graph represents a function if and only if no vertical line intersects the graph at more than one point.
Let’s analyze each graph:
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Top Graph: The graph is a parabola. Applying the vertical line test, some vertical lines (e.g., near the vertex) intersect the graph twice. Therefore, this is NOT a function.
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Middle Graph: This graph is a curve extending upwards. Some vertical lines will intersect the graph at more than one point (e.g., near the center of the curve). This is NOT a function.
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Bottom Graph: This graph is a straight line. Any vertical line intersects the graph only once. This IS a function.
Would you like further clarification or detailed explanations? Let me know if you have more questions!
Here are related questions to deepen your understanding:
- What is the definition of a function in mathematics?
- How does the vertical line test work for identifying functions?
- Are all straight-line graphs always functions? Why or why not?
- How can you algebraically confirm if a relation is a function?
- Can a relation fail the vertical line test but still have some functional properties?
Tip: Always visualize or sketch graphs if unsure about the vertical line test—it’s an intuitive and reliable method!
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Math Problem Analysis
Mathematical Concepts
Functions
Graphs
Vertical Line Test
Formulas
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Theorems
Vertical Line Test
Suitable Grade Level
Grades 8-10
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