a)First, we have to rewrite the function m(x) in the form \(\displaystyle{m}{\left({x}\right)}=\sqrt{{{x}—{h}}}+{k}\)

So, the steps are: factor the radicand, use the Product Property of Radicals and than simplify, so, we have next:

\(\displaystyle{m}{\left({x}\right)}=\sqrt{{{7}{\left({x}-{0.5}\right)}}}-{10}\)

\(\displaystyle=\sqrt{{7}}\cdot\sqrt{{{x}-{0.5}}}-{10}\)

\(\displaystyle={2.65}\sqrt{{x}}={0.5}-{10}\)

So, the graph of m(x) is a vertical stretch of a parent function by a factor of 2.65 or \(\displaystyle\sqrt{{7}}\), translated right 0.5 units and translated down 10 units. On the following picture there is a graph of \(\displaystyle{y}=\sqrt{{x}}{\quad\text{and}\quad}{m}{\left({x}\right)}=\sqrt{{{7}{x}-{3.5}}}-{10}\)

b)First, we have to rewrite the function j(x) in the form: \(\displaystyle{j}{\left({x}\right)}={a}\sqrt{{{x}-{h}}}+{k}\) So, the steps are: use the Product Property of Radicals and than simplify, so we have next:

\(\displaystyle{j}{\left({x}\right)}=-{2}\sqrt{{{4}\cdot{3}\cdot{x}}}+{4}\)

\(\displaystyle=-{2}\sqrt{{4}}\cdot\sqrt{{3}}\cdot\sqrt{{x}}+{4}\)

\(\displaystyle=-{2}\cdot{2}\cdot\sqrt{{3}}\cdot\sqrt{{x}}+{4}\)

\(\displaystyle=-{4}\sqrt{{3}}\cdot\sqrt{{x}}+{4}\)

So, the graph of j(x) is a vertical stretch of a parent function by a factor of \(\displaystyle-{4}\sqrt{{3}}\), translated up 4 units.