Math Problem Statement
Solution
The task in the image asks to determine whether each graph represents a function. To assess this, we can apply the vertical line test: a graph represents a function if and only if no vertical line can intersect the graph at more than one point at a time.
Let's analyze each graph:
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Gráfico 1: The vertical line test shows multiple points on a single vertical line (for example, around ). Therefore, this is not a function.
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Gráfico 2: Any vertical line drawn will intersect the graph at only one point. Hence, this is a function.
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Gráfico 3: A vertical line can intersect the graph in multiple places (for instance, near ). This is not a function.
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Gráfico 4: Several vertical lines intersect more than one point (for example, ). This is not a function.
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Gráfico 5: Every vertical line intersects the graph at most once. Hence, this is a function.
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Gráfico 6: A vertical line intersects the graph at multiple points (such as near ). Therefore, this is not a function.
If you would like more details or have further questions, let me know!
Here are 5 related questions to explore the topic further:
- What are the key characteristics of a function in terms of domain and range?
- How does the vertical line test relate to the definition of a function?
- Can a horizontal line test be applied to check if a graph is a one-to-one function?
- How do transformations (shifting, reflecting) affect whether a graph represents a function?
- What are some real-world examples where we need to determine if a relation is a function?
Tip: Always apply the vertical line test to quickly verify if a graph represents a function!
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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 9-11
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