Evaluate f(x) = x^2 at x = -3. What is f(-3)?

• A. 4
• B. 8
• C. 9
• D. 16

Answer: (C)

Evaluating a function at an input means substituting that value for x and simplifying. For f(x) = x^2, f(-3) is (-3)^2. Multiply -3 by -3 to obtain 9; a negative times a negative is positive, so the sign disappears. Squares are nonnegative, and the output depends only on the magnitude of the input, not its sign, so -3 and 3 give the same result. Thus the value is 9. The other numbers would come from squaring different inputs, like -2 or 2 for 4, or -4 or 4 for 16, or they could come from a non-square operation, which isn’t the case here.