Problem 114 - Precalculus Essentials

Question

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

Step-by-Step Solution

Answer

The vertical line test is a method used to determine whether a graph represents a function. This is done by imagining or drawing a vertical line through every point on the graph. If every one of these lines intersects the graph at exactly one point, then the graph represents a function. If any line intersects the graph more than once, the graph does not represent a function.

Step 1: Understand what a function is

A function is a special type of relation where each input (or 'x' value) has exactly one output (or 'y' value). This means that for each value from the domain, there should be only one corresponding value in the codomain. This sets the foundation for the vertical line test.

Step 2: Describe the vertical line test

The vertical line test is a method to determine if a graph represents a function. This test involves imagining or drawing a vertical line through each and every point on the graph. The graph passes the vertical line test and thus represents a function if every vertical line intersects the graph in exactly one point.

Step 3: Apply the vertical line test

To apply the test, draw vertical lines on the graph at various points along the x-axis. If at any point the line intersects the graph at more than one point, the graph does not represent a function, since that would mean an 'x' value would have more than one corresponding 'y' value.