Functions

Domain and Range

Identify possible input values and output values.

Functions overviewTransformationsModulus functions

Definitions

Domain

The set of allowed input values, usually \(x\)-values.

Range

The set of possible output values, usually \(y\)-values.

domain: x-valuesrange: y-values
Project the curve onto the x-axis for the domain and onto the y-axis for the range.

Worked example

Find the domain of \(f(x)=\sqrt{x-3}\).

The expression under the square root must be non-negative:

\[x-3\ge 0\Rightarrow x\ge 3.\]

So the domain is \([3,\infty)\).