Math Problem Statement

Is this a function?

Is this a function?

Solution

The image shows a graph of a circle in the plane. To determine if the given relation is a function, we can apply the Vertical Line Test. This test states that a graph represents a function if no vertical line intersects the graph more than once.

In the image, we see a vertical dashed line at x=2x = 2, which intersects the circle at two points. Since the vertical line crosses the graph more than once, this means that for some values of xx, there are multiple values of f(x)f(x).

Thus, this graph does not represent a function because it fails the vertical line test.

Would you like more details on this? Here are some related questions you might find interesting:

  1. What is the vertical line test and why does it determine if a graph is a function?
  2. How can you tell if a relation is a function by looking at its equation?
  3. What is the equation of a circle and how does it differ from a function?
  4. How can we modify this graph so that it represents a function?
  5. Are there special cases where a relation can still be considered a function even if the vertical line test fails?

Tip: A function must assign only one output value for each input value, which is why passing the vertical line test is crucial for determining whether a graph represents a function.

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Math Problem Analysis

Mathematical Concepts

Functions
Graph Theory

Formulas

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Theorems

Vertical Line Test

Suitable Grade Level

Grades 8-10