Evaluating Functions


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Functions describe relationships between variables. A function answers the question, “What happens to y when we change the value of x?” In a function, there will be a specific mathematical relationship between these variables. For any given value of x, there will only be one possible value for y.

To evaluate a function means to find the output when you plug in an input. In other words, evaluating a function is finding the value of y when you know the value of x. Evaluating functions is very similar to solving equations. Let's look at the step-by-step process of evaluating functions and then look at an example.

These are the basic steps for evaluating functions:

  1. Identify the function. Functions are usually written as f(x) or g(x), where x is the input variable. We often say this as “the function of x” or “f of x.” [Example: f(x) =
  2. Plug in the input number. Replace every x in the function with the input value you want to evaluate.
  3. Simplify the expression. Combine like terms and do any math operations needed. This gives you one output value.
  4. The result is your output! This is the function's value when you plug in that input.

How about an example? Let's evaluate f(x) = 2x + 3 when x = 5.

  • Step 1: The rule is f(x) = 2x + 3.
  • Step 2: Plug in x = 5: f(5) = 2(5) + 3
  • Step 3: Simplify: f(5) = 10 + 3 = 13
  • Step 4: The output is 13. So f(5)=13