To plot the graph of the given function we will use the graph of \(\displaystyle{y}=\sqrt{{{x}}}.\) We take the following steps. First we shift the graph of VT horizontally by 3 units to the left.This gives us the graph of m Next, we stretch the graph vertically by a factor of 2.After that, we reﬂect the graph around the x-axis.

Finally, we shift the graph of

\(\displaystyle-{2}\sqrt{{{x}+{3}}}\)

1 unit upward and obtain the graph of

\(\displaystyle{y}={1}-{2}\sqrt{{{x}+{3}}}\)

The hand-sketched graph is given bellow. Also we provide the graph obtained by using CAS.

Finally, we shift the graph of

\(\displaystyle-{2}\sqrt{{{x}+{3}}}\)

1 unit upward and obtain the graph of

\(\displaystyle{y}={1}-{2}\sqrt{{{x}+{3}}}\)

The hand-sketched graph is given bellow. Also we provide the graph obtained by using CAS.