For a function to be one-to-one, it must pass which line tests?

For a function to be one-to-one, it must pass which line tests?

• A. Vertical only
• B. Horizontal only
• C. Vertical and horizontal
• D. Neither

Answer: (C)

A one-to-one function is about distinct inputs giving distinct outputs. On a graph, that means it must be a function (each input has one output) and injective (no two inputs share the same output). The vertical line test checks that the graph is a function: no vertical line should intersect the graph more than once. The horizontal line test checks that the function is injective: no horizontal line should intersect the graph more than once. Therefore, to be one-to-one, the graph must pass both tests—hence vertical and horizontal. If a horizontal line hits the graph at two different x-values, you’d have two inputs producing the same output; if a vertical line hits the graph at more than one point, it isn’t a function to begin with.

A one-to-one function is about distinct inputs giving distinct outputs. On a graph, that means it must be a function (each input has one output) and injective (no two inputs share the same output). The vertical line test checks that the graph is a function: no vertical line should intersect the graph more than once. The horizontal line test checks that the function is injective: no horizontal line should intersect the graph more than once. Therefore, to be one-to-one, the graph must pass both tests—hence vertical and horizontal. If a horizontal line hits the graph at two different x-values, you’d have two inputs producing the same output; if a vertical line hits the graph at more than one point, it isn’t a function to begin with.