In evaluating a function f(x), what does f(3) represent?

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Multiple Choice

In evaluating a function f(x), what does f(3) represent?

Explanation:
Evaluating a function at a specific input means substituting that input into the function and computing the result. f(3) is the value the function outputs when the input is 3. In other words, plug x = 3 into f and simplify to get a number. That number belongs to the function’s range and represents the output corresponding to the input 3 in the domain. The slope at x = 3 would come from the derivative f′(3), which is a different concept, not what f(3) gives. For example, if f(x) = x^2 + 2, then f(3) = 9 + 2 = 11, so the output is 11.

Evaluating a function at a specific input means substituting that input into the function and computing the result. f(3) is the value the function outputs when the input is 3. In other words, plug x = 3 into f and simplify to get a number. That number belongs to the function’s range and represents the output corresponding to the input 3 in the domain. The slope at x = 3 would come from the derivative f′(3), which is a different concept, not what f(3) gives. For example, if f(x) = x^2 + 2, then f(3) = 9 + 2 = 11, so the output is 11.

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