### Functions: Power functions and root functions

### Root function

Root function

The simplest **root function** is the function \[f(x)=\sqrt{x}\]

The table with this root function is (all roots rounded to 2 decimals):

#\begin{array}{c|c|c|c|c|c|c|c}

x & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\

\hline y & 0 & 1 & 1.41 & 1.73 & 2 & 2.24 & 2.45

\end{array}#

The graph of the function is half a parabola with **origin **#\rv{0,0}#.

Since the root is only defined for non-negative numbers, the domain of the root function is equal to the interval #\ivco{0}{\infty}#.

Since the root of a non-negative number is a non-negative number in itself, the range is also equal to the interval #\ivco{0}{\infty}#.

Take a look at the function #f(x)=\sqrt{x}#. Does the point #\rv{4, 2}# lie on the graph on this function?

In here, you can round the #y#-value of the point to #2# decimals, if needed.

In here, you can round the #y#-value of the point to #2# decimals, if needed.

Yes

We substitute #x=4# in the formula. This is done in the following way:

\[f(4)=\sqrt{4}=2\]

Hence, #\rv{4, 2}# is a point on the graph.

We substitute #x=4# in the formula. This is done in the following way:

\[f(4)=\sqrt{4}=2\]

Hence, #\rv{4, 2}# is a point on the graph.

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