Which statement about the one-to-one property is correct?

Which statement about the one-to-one property is correct?

• A. Passes vertical line test only.
• B. Passes horizontal line test only.
• C. Passes both vertical and horizontal line tests.
• D. Passes neither line test.

Answer: (C)

One-to-one means each output value comes from exactly one input value. On a graph, that translates to no horizontal line intersecting the graph more than once, because multiple intersections at the same height would give the same y value from different x values. But to be a function in the first place, the graph must pass the vertical line test, so every x corresponds to at most one y. Therefore, a one-to-one function must pass both tests: the vertical line test and the horizontal line test. That’s why the statement describing it as passing both tests is the best answer. For example, y = x passes both tests (one-to-one), while y = x^2 passes the vertical line test but fails the horizontal line test for positive y values, so it is not one-to-one.

One-to-one means each output value comes from exactly one input value. On a graph, that translates to no horizontal line intersecting the graph more than once, because multiple intersections at the same height would give the same y value from different x values. But to be a function in the first place, the graph must pass the vertical line test, so every x corresponds to at most one y. Therefore, a one-to-one function must pass both tests: the vertical line test and the horizontal line test. That’s why the statement describing it as passing both tests is the best answer. For example, y = x passes both tests (one-to-one), while y = x^2 passes the vertical line test but fails the horizontal line test for positive y values, so it is not one-to-one.