Function Notation and Evaluating Functions
Simple Explanation
Function notation, f(x), names a function f and shows what it does to an input x. To "evaluate" f at a specific number, substitute that number everywhere x appears in the function's rule, then simplify.
Why Do We Need It?
f(x) notation is used throughout mathematics and science to name and apply functions precisely — reading and evaluating it correctly is a foundational skill for every function-based topic that follows.
Worked Example
Evaluate a function at a given input
If f(x) = 2x² − 3x + 1, find f(4).
Why Does This Work?
f(x) is just a name for "the output the rule produces from input x" — substituting a specific number for x and carrying out the arithmetic directly computes that output, by the definition of the notation.
Real-Life Example
A currency conversion function
A currency converter can be written as a function C(d), giving the local-currency value of d US dollars.
Evaluating C(50) means substituting d = 50 into the conversion rule — exactly the same substitution process used for any function notation.
Practice
If f(x) = 5x − 2, find f(6).
MediumIf g(x) = x² + 2x, find g(-3).
MediumCommon mistake
Misreading f(x) as "f multiplied by x" — f(x) is function notation, naming an output, not a multiplication; f(4) means "the output of f when the input is 4", not "f times 4".
Quick Review
- f(x) names the output that function f produces from input x.
- Evaluate f at a number by substituting it for every x in the rule, then simplifying.
- f(x) is notation for a function's output, never a multiplication of f and x.