What does the vertical line test determine about a graph?

What does the vertical line test determine about a graph?

• A. Whether the graph crosses the x-axis
• B. Whether it is a continuous function
• C. If it is a function based on how many times it is crossed by a vertical line
• D. If the graph supports rational expressions

Answer: (C)

The vertical line test is a method used to determine if a graph represents a function. A function is defined as a relation in which each input (or x-value) corresponds to exactly one output (or y-value). When you apply the vertical line test, you imagine drawing vertical lines through the graph at various x-values. If any vertical line crosses the graph more than once, it indicates that there are multiple y-values for that particular x-value, which violates the definition of a function. Therefore, passing the vertical line test confirms that for every x-value in the domain of the graph, there is exactly one corresponding y-value, indicating that the graph indeed represents a function. This is why the correct answer is that the test determines if the graph is a function based on how many times it is crossed by a vertical line. In summary, the vertical line test is a clear and visual way to verify a key property of functions, ensuring that the relationship between x and y is properly defined.

The vertical line test is a method used to determine if a graph represents a function. A function is defined as a relation in which each input (or x-value) corresponds to exactly one output (or y-value). When you apply the vertical line test, you imagine drawing vertical lines through the graph at various x-values.

If any vertical line crosses the graph more than once, it indicates that there are multiple y-values for that particular x-value, which violates the definition of a function. Therefore, passing the vertical line test confirms that for every x-value in the domain of the graph, there is exactly one corresponding y-value, indicating that the graph indeed represents a function. This is why the correct answer is that the test determines if the graph is a function based on how many times it is crossed by a vertical line.

In summary, the vertical line test is a clear and visual way to verify a key property of functions, ensuring that the relationship between x and y is properly defined.