### Functions: Domain and range

### Range

Take a look at the function #f(x)=x^2#.

We see that the smallest value this function takes on is #0#, after that the function increases indefinitely.

Hence all values in the interval #\ivco{0}{\infty}# are *within range* of the function.

We say that the **range **of #f# is equal to the interval #\ivco{0}{\infty}#.

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Range

The **range** of a function #f# consists of all values #f(x)# that this function can reach on its domain.

**Example**

Determine the range of #f(x)=-x^2#:

the interval #(-\infty, 0]#

The range is: #\ivco{-4}{\infty}#

We sketch the graph:

We can read the range from the sketch.

The smallest function value is #-4# and after that the graph increases indefinitely.

The range is: #\ivco{-4}{\infty}#.

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