Given a graph of
we can sketch the graph
equivalent to
by making the following observations.
cannot be negative since we cannot take the square root of a negative number to obtain a real number. Ifis negative for any value of
these values of
do not appear in the domain of
and these points cannot be plotted. Any parts of the graph for which
must be discarded.When we take the square root, if
then we have two y values, equal in magnitude and opposite in sign. We plot the points
and
The– axis becomes a line of symmetry.Any roots
remain roots of
Values of
less than 1 will be increased after square rooting and values ofgreater than 1 will be decreased.
Example: Sketch the graph of
The graph ofis shown below.
The graph ofis shown below.
