Math Problem Statement

Determine whether each graph represents a function.

Solution

To determine whether each graph represents a function, we can apply the vertical line test. This test states that if a vertical line can intersect the graph in more than one point at any location, the graph is not a function.

Here’s an analysis for each graph:

  1. First Graph (left-most): This is a straight, diagonal line. Any vertical line drawn on this graph will only intersect the graph at one point. Therefore, this graph represents a function.

  2. Second Graph (parabolic shape): This graph shows a curve that opens horizontally. A vertical line drawn through certain points on this graph would intersect the curve in more than one place. Thus, this graph does not represent a function.

  3. Third Graph (scatter plot with distinct points): Each x-value has only one corresponding y-value, as it is a set of individual points. No vertical line would intersect more than one point. Therefore, this graph represents a function.

  4. Fourth Graph (scatter plot with multiple points aligned vertically): This graph has multiple points that share the same x-values. Thus, a vertical line can intersect more than one point on this graph, which means it does not represent a function.

Conclusion:

  • Function: First and Third graphs
  • Not a Function: Second and Fourth graphs

Would you like further details or have any questions?


Related Questions:

  1. What is the vertical line test, and why is it effective for determining functions?
  2. How can we determine if a graph of an equation represents a function algebraically rather than graphically?
  3. Why does a horizontal parabola fail the function test but a vertical one passes?
  4. How do discrete points in a graph affect the determination of a function?
  5. Can you explain why a function cannot have multiple outputs for a single input?

Tip: For a function, each x-value must correspond to only one y-value.

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Math Problem Analysis

Mathematical Concepts

Functions
Vertical Line Test
Graphs

Formulas

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Theorems

Vertical Line Test

Suitable Grade Level

Grades 8-10