ANSWER:
a.
b.
STEP-BY-STEP EXPLANATION:
We have the following functions:
[tex]\begin{gathered} f\mleft(x\mright)=\sqrt{x} \\ g\mleft(x\mright)=\sqrt{x+4} \\ h\mleft(x\mright)=\sqrt{x}+4 \end{gathered}[/tex]
a.
We calculate all the values for each function.
For f(x):
[tex]\begin{gathered} f\mleft(0\mright)=\sqrt[]{0}=0 \\ f(4)=\sqrt{4}=2 \\ f(8)=\sqrt{8}=2\sqrt{2} \\ f(16)=\sqrt[]{16}=4 \end{gathered}[/tex]
For g(x):
[tex]\begin{gathered} g\mleft(0\mright)=\sqrt[]{0+4}=\sqrt[]{4}=2 \\ g(4)=\sqrt[]{4+4}=\sqrt[]{8}=2\sqrt{2} \\ g(8)=\sqrt[]{8+4}=\sqrt[]{12}=2\sqrt{3} \\ g(16)=\sqrt[]{16+4}=\sqrt[]{20}=2\sqrt{5} \end{gathered}[/tex]
For h(x):
[tex]\begin{gathered} h\mleft(0\mright)=\sqrt[]{0}+4=0+4=4 \\ h(4)=\sqrt[]{4}+4=2+4=6 \\ h(8)=\sqrt[]{8}+4=2\sqrt{2}+4 \\ h(16)=\sqrt[]{16}+4=4+4=8 \end{gathered}[/tex]
Now, we fill the table with the obtained values:
b.
To graph on the Cartesian plane, what we do is locate the points and then draw the line between these points to obtain the graph, like this:
