Set a(x)=(1/2)^x; then,

Furthermore,

Then, the parent function of function 1) is (1/2)^x.
On the other hand, if b(x)=3^x; then,

Therefore, the parent function of 2*3^x is 3^x.
Now, we need to find 9 points on each parent function, as shown below

And

After graphing the points, we get
Parent function of function 1)
Parent function of function 2)
Now, translating the parent function in green two units to the right and 1 unit up, we obtain
In both images, the green curve is 1/2^(x)->parent function of (1/2)^(x-2)+1
the yellow curve is (1/2)^(x-2)+1
The red curve is 3^x->parent function of 2*3^x
and the blue curve is 2*3^x