Which statement correctly defines a function?

Which statement correctly defines a function?

• A. Every x-value maps to more than one y-value.
• B. A relation that has at least two distinct y-values for the same x-value.
• C. The graph of a function is always a straight line.
• D. Every x-value maps to exactly one y-value.

Answer: (D)

The key idea is that a function assigns exactly one output to every input. That means for every x value you choose, there should be one and only one y that goes with it. If an x value can pair with multiple y values, it isn’t a function. The graph being a straight line isn’t required—functions can be curved, like y = x^2. A quick way to check is the vertical line test: if a vertical line crosses the graph more than once, that x would have more than one y, so it’s not a function. So the statement that matches this idea is that every x-value maps to exactly one y-value.

The key idea is that a function assigns exactly one output to every input. That means for every x value you choose, there should be one and only one y that goes with it. If an x value can pair with multiple y values, it isn’t a function. The graph being a straight line isn’t required—functions can be curved, like y = x^2. A quick way to check is the vertical line test: if a vertical line crosses the graph more than once, that x would have more than one y, so it’s not a function. So the statement that matches this idea is that every x-value maps to exactly one y-value.