I do not understand the parent functions I've tried many times but get confused I just need a step-by-step explanation if you can thank you!

We will find the points:
1)
[tex]f(x)=(\frac{1}{2})^{x-2}+1[/tex][tex]\begin{cases}f(-4)=65 \\ f(-3)=33 \\ f(-2)=17 \\ f(-1)=9 \\ f(0)=5 \\ f(1)=3 \\ f(2)=2 \\ f(3)=\frac{3}{2} \\ f(4)=\frac{5}{4}\end{cases}[/tex]2)
[tex]f(x)=2\cdot3^x[/tex][tex]\begin{cases}f(-4)=\frac{2}{81} \\ f(-3)=\frac{2}{27} \\ f(-2)=\frac{2}{9} \\ f(-1)=\frac{2}{3} \\ f(0)=2 \\ f(1)=6 \\ f(2)=18 \\ f(3)=54 \\ f(4)=162\end{cases}[/tex]