Under what condition does the vertical line test indicate a function is one to one?

Under what condition does the vertical line test indicate a function is one to one?

• A. If it intersects more than one point
• B. If it intersects exactly one point
• C. If it is parallel to the x-axis
• D. If it crosses the y-axis

Answer: (B)

The vertical line test is primarily used to determine whether a graph represents a function. However, when considering whether a function is one-to-one, the relevant concept is not the vertical line test but rather the horizontal line test. For clarity, a one-to-one function is defined as a function where each output is paired with exactly one input. In this context, if a horizontal line intersects the graph of a function at exactly one point, the function is one-to-one. Therefore, option B, which states, "If it intersects exactly one point," aligns closely with this condition but in the context of the horizontal line test rather than the vertical line test. The vertical line test indicates a function is defined (it is not the condition for being one-to-one). This method simply checks that any vertical line drawn through the graph intersects it at no more than one point, confirming that the relation is indeed a function. Thus, while option B addresses a situation that applies to one-to-one functions under the horizontal line test, the vertical line test itself does not determine if a function is one-to-one. Instead, it confirms the existence of a function in the first place.

The vertical line test is primarily used to determine whether a graph represents a function. However, when considering whether a function is one-to-one, the relevant concept is not the vertical line test but rather the horizontal line test. For clarity, a one-to-one function is defined as a function where each output is paired with exactly one input.

In this context, if a horizontal line intersects the graph of a function at exactly one point, the function is one-to-one. Therefore, option B, which states, "If it intersects exactly one point," aligns closely with this condition but in the context of the horizontal line test rather than the vertical line test.

The vertical line test indicates a function is defined (it is not the condition for being one-to-one). This method simply checks that any vertical line drawn through the graph intersects it at no more than one point, confirming that the relation is indeed a function. Thus, while option B addresses a situation that applies to one-to-one functions under the horizontal line test, the vertical line test itself does not determine if a function is one-to-one. Instead, it confirms the existence of a function in the first place.