Math Problem Statement

Determine if each graph represents a function using the vertical line test.

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:

  1. Gráfico 1: The vertical line test shows multiple points on a single vertical line (for example, around x=1x = 1). Therefore, this is not a function.

  2. Gráfico 2: Any vertical line drawn will intersect the graph at only one point. Hence, this is a function.

  3. Gráfico 3: A vertical line can intersect the graph in multiple places (for instance, near x=0x = 0). This is not a function.

  4. Gráfico 4: Several vertical lines intersect more than one point (for example, x=1x = -1). This is not a function.

  5. Gráfico 5: Every vertical line intersects the graph at most once. Hence, this is a function.

  6. Gráfico 6: A vertical line intersects the graph at multiple points (such as near x=1x = 1). 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:

  1. What are the key characteristics of a function in terms of domain and range?
  2. How does the vertical line test relate to the definition of a function?
  3. Can a horizontal line test be applied to check if a graph is a one-to-one function?
  4. How do transformations (shifting, reflecting) affect whether a graph represents a function?
  5. 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