Functions

Function Notation

A function f assigns one output to each input. Evaluate f(x)=2x²-3x+1 at x=4 by substituting: 2(16)-12+1=21.

function-notation f(x) means "f evaluated at x." Substitute the input value for every x, then simplify using order of operations.

Example

Evaluate a function by substituting the input value for x.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

f(x)=2x2−3x+1f(x)= 2x^{2} - 3x + 1

Step 2 — Substitute input

Substitute 4 for x in 2x squared minus 3x plus 1.

f(4)=2(4)2−3(4)+1f( \hl{4} )= 2 ( 4 )^{ 2 }- 3 ( 4 )+ 1

Step 3 — Square input

Square the input: 4^2 = 16.

42=164 ^{ 2 }= \hl{16}

Step 4 — Multiply terms

Multiply terms: 2 times 16, then subtract 12 and add 1.

2⋅16−12+12 \cdot \hl{16} - \hl{12} + 1

Step 5 — Result

The function value is f(4) = 21.

f(4)=21f( 4 )= \hl{21}