The range is the set of all the possible values of the dependent variable.
The range of a function is the complete set of output values the function can produce. If we think of a function as a machine, where numbers go in, a rule is applied, and results come out, the range is every possible result that machine can generate.
For example, consider the function f(x) = x². No matter what value of x we put in, the output is always zero or positive (since any number squared is non-negative). So the range is all numbers greater than or equal to 0.
The range works alongside the domain, which is the set of all possible input values. Together, they describe a function completely:
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Domain: what can go in
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Range: what can come out
On a graph, the domain appears along the horizontal axis (x-axis) and the range appears along the vertical axis (y-axis). The range is the set of all y-values the graph actually reaches.
When Do Students Learn About the Range of a Function?
Students build toward the range of a function through their work with input-output tables and graphing.
Grades 6–8 – Output Values and Functions
Students work with output values in tables and graphs, identifying what results a rule or function produces — direct preparation for understanding range formally.
Grades 9+ – Domain and Range in Advanced Functions
Students identify the range of linear, quadratic, exponential, and other function types, analyzing graphs and equations to determine which output values are possible.
