Domains and Ranges of Standard Functions Set 1

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Listed below are some functions we’ll encounter frequently. Note carefully their domains and ranges and how they have been plotted.

1. Constant function \(f\,(x) = k\)

Domain = \(\mathbb{R}\)

Range = \(\{ k\} \)

Constant function graph
 

2. Identity function \(f\,(x) = x\)

Domain = \(\mathbb{R}\)

Range = \(\mathbb{R}\)

Identity function graph

 

3. Linear function \(f\,(x) = mx + c\)

Domain = \(\mathbb{R}\)

Range = \(\mathbb{R}\)

Linear function graph

 

4. Square function \(f\,(x) = {x^2}\)

Domain = \(\mathbb{R}\)

Range = [0, \(\infty\))

Square function graph

5. Cube function \(f\,(x) = {x^3}\)

Domain = \(\mathbb{R}\)

Range = \(\mathbb{R}\)

Cube function graph