Explain how the vertical line test is used to determine whether a graph represents a function.

The vertical line test is a visual way to determine if a graph represents a function. Here's how it works:

Step 1: Define the Problem

Identify the key concept: determining if a graph represents a function using the vertical line test.

Step 2: Break Down the Problem

Understand the criteria for a function: A function has only one output (y-value) for each input (x-value).

Step 3: Apply Relevant Concepts

• Vertical Line Test: Draw vertical lines across the graph. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

Step 4: Analysis, Verify and Summarize

• Analysis: By intersecting the graph at multiple points, a vertical line indicates that a single x-value corresponds to multiple y-values, which violates the definition of a function.
• Verification: Ensure that no vertical line intersects the graph more than once to confirm it represents a function.

Final Answer

The vertical line test is used to determine if a graph represents a function by checking that no vertical line intersects the graph at more than one point. If it does, the graph is not a function.