The horizontal line test determines whether a function is:

The horizontal line test determines whether a function is:

• A. Determines if a function is one-to-one
• B. Determines if a function is continuous
• C. Determines if a function is differentiable
• D. Determines if a function is surjective

Answer: (A)

The horizontal line test checks whether each horizontal line intersects the graph in at most one point, which is exactly the definition of a one-to-one (injective) function. If every horizontal line hits the graph at most once, each output value comes from a unique input, so the function is one-to-one. If some horizontal line crosses the graph more than once, that means two different inputs produce the same output, so the function is not one-to-one. This test does not address continuity, differentiability, or surjectivity. For example, x^2 is continuous and differentiable everywhere but fails the horizontal line test because y = 1 meets the graph at two points, showing it’s not one-to-one. Conversely, the exponential function e^x passes the horizontal line test and is injective, though surjectivity depends on the specified codomain.

The horizontal line test checks whether each horizontal line intersects the graph in at most one point, which is exactly the definition of a one-to-one (injective) function. If every horizontal line hits the graph at most once, each output value comes from a unique input, so the function is one-to-one. If some horizontal line crosses the graph more than once, that means two different inputs produce the same output, so the function is not one-to-one.

This test does not address continuity, differentiability, or surjectivity. For example, x^2 is continuous and differentiable everywhere but fails the horizontal line test because y = 1 meets the graph at two points, showing it’s not one-to-one. Conversely, the exponential function e^x passes the horizontal line test and is injective, though surjectivity depends on the specified codomain.