Math Problem Statement

Which graph represents a function?

Solution

The vertical line test is used to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, the graph does not represent a function.

In the image you provided, here’s an analysis of the graphs:

  1. First graph (Leftmost): This graph shows an arrow pointing straight upward, which suggests a vertical line. A vertical line fails the vertical line test since it intersects at infinitely many points. This is not a function.

  2. Second graph (Middle-left): This graph shows a curve that appears to pass the vertical line test. Any vertical line drawn will intersect the graph at exactly one point. This is a function.

  3. Third graph (Middle-right): This graph shows a horizontal line. A horizontal line always passes the vertical line test because a vertical line would intersect it at only one point. This is a function.

Therefore, the second and third graphs represent functions. Based on the multiple-choice format of the image, the second graph (Middle-left) is the most likely intended answer for the question.

Would you like further clarification on the vertical line test or other topics?

Here are 5 related questions:

  1. How does the vertical line test apply to real-world functions?
  2. Can a graph be a function if it intersects the y-axis multiple times?
  3. How is the vertical line test related to the concept of a "one-to-one" function?
  4. What is the horizontal line test, and how does it differ from the vertical line test?
  5. Can a circle ever represent a function?

Tip: Remember, for a graph to represent a function, each input (x-value) must correspond to exactly one output (y-value).

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Math Problem Analysis

Mathematical Concepts

Functions
Graphical Analysis of Functions

Formulas

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Theorems

Vertical Line Test

Suitable Grade Level

Grades 9-12