Which graph represents a function

3. Which graph represents a function? Explain.

The Correct Answer and Explanation is :

To determine which graph represents a function, we can apply the vertical line test. This test states that if any vertical line intersects the graph at more than one point, the graph does not represent a function. Conversely, if every vertical line intersects the graph at exactly one point, the graph represents a function. citeturn0search0

In the provided image, there are three graphs labeled A, B, and C. By applying the vertical line test to each:

• Graph A: A vertical line intersects the graph at more than one point, indicating that this graph does not represent a function.
• Graph B: A vertical line intersects the graph at exactly one point, suggesting that this graph represents a function.
• Graph C: A vertical line intersects the graph at more than one point, meaning this graph does not represent a function.

Therefore, Graph B represents a function.

Explanation:

A function is a relation where each input (x-value) corresponds to exactly one output (y-value). The vertical line test is a visual method to determine if a graph represents a function:

1. Draw Vertical Lines: Imagine or draw vertical lines at various x-values across the graph.
2. Check Intersections: Observe how many times each vertical line intersects the graph.
3. Interpret Results:

• If any vertical line intersects the graph at more than one point, the graph does not represent a function.
• If every vertical line intersects the graph at exactly one point, the graph represents a function.

This test is effective because it ensures that for each x-value, there is only one corresponding y-value, which is the defining characteristic of a function.

For a visual demonstration and further clarification, you might find the following video helpful:

videoHow to tell if a Graph Represents a Functionturn0search1