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{7, -0.15}# 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.
No
We substitute #x=7# in the formula. This is done in the following way:
\[f(7)=\sqrt{7}=2.65\]
Hence, #\rv{7, -0.15}# is not a point on the graph.
We substitute #x=7# in the formula. This is done in the following way:
\[f(7)=\sqrt{7}=2.65\]
Hence, #\rv{7, -0.15}# is not a point on the graph.
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