Function Notation Evaluation

Function notation evaluation

Function notation tells you which input to use in a rule or formula. The expression (f(x)) means “the value of the function (f) when the input is (x).” Your goal is to replace the variable inside the function with the given number or expression, then simplify.

Method

1. Identify the input in the problem. This may be a number, such as (f(3)), or an expression, such as (f(a+2)).
2. Substitute carefully into the function rule. Replace every occurrence of the input variable with the given value.
3. Use parentheses when the input is an expression. This helps you avoid sign and distribution errors.
4. Simplify the result using order of operations.

Helpful checks

• If the answer is numerical, plug it back into the function rule if possible to see whether the output makes sense.
• If the input is a variable expression, make sure you substituted the entire expression, not just part of it.
• Watch for negative signs and exponents; they often change the result.

Example idea

If (f(x)=2x+5), then (f(3)=2(3)+5=11). The same idea works for any function rule: substitute first, simplify second.