Range of a function

The range of a function is the set of all possible values it can produce.
For example, consider the function No matter what value we give to x, the function is always positive:

  • If x is 2, then the function returns x squared or 4.
  • If x is negative 2, then it still produces 4 since -2 times -2 is positive 4.

So the range of the function is

"all real numbers greater than or equal to zero".


Ranges can be written out in words as above, but to be more mathematically precise they are also written using either inequalities, or in interval notation:

  • As an inequality, we would write Which is read as "the function f(x) has a value which is always greater than or equal to zero".
    For more on inequalities see Inequalities.

  • In so-called interval notation, the same function has a range of This describes the range of values from 0 to positive infinity. The square brackets means the range includes zero and infinity themselves.

As a graph

graph of x squared If we plot the function above on a graph we see that for any value of x, the graph is either zero or positive - above the x axis.

Other functions topics