Problem 114 - College Algebra 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 used to check if a graph represents a function. If we can draw a vertical line that intersects the graph more than once, the graph does not represent a function since that would mean one input ('x' value) is linked to more than one output ('y' value).

Step 1: Understanding Vertical Line Test

The Vertical Line Test is a visual way to use a vertical line to determine if a graph represents a function. A function is a particular type of relation where every input (or 'x' value) corresponds to exactly one output (or 'y' value).

Step 2: Defining the Rule of Vertical Line Test

The rule of Vertical Line Test is simply stated as: If any vertical line intersects the graph more than once, then the graph does not represent a function. This is because, if the vertical line intersects the graph at more than one point, it means that a single input ('x' value) has more than one output ('y' value).

Step 3: Applying the Vertical Line Test

If you are given a graph and want to use the Vertical Line Test to check if the graph represents a function, you need to draw or visualize vertical lines across the graph. If there's any vertical line that intersects the graph at more than one point, the graph does not represent a function. Otherwise, it does.