Range of a Function

The range of a function is the set of all output values (also known as y-values) when all elements of the domain are evaluated into the function.

Example: What is the range of the function $y = {x^2} + 2$ ?

The best way to find the range of a function is to graph it on the xy-plane.

a graph of a quadratic function with a range of y≥2

By observing the graph of the function, the lowest value of $y$ is $3$ and it goes up to positive infinity. Therefore we can say that the range of the given function is greater than or equal to $2$ .

In set notation we have,

Range: $\left\{ {y \in \Re |y \ge 2} \right\}$

We can read this as “y is an element of the Real Numbers such that y is greater than or equal to 2“.

Range of a Function

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