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:
- 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) =
- Plug in the input number. Replace every x in the function with the input value you want to evaluate.
- Simplify the expression. Combine like terms and do any math operations needed. This gives you one output value.
- 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