Describe the transformations from the parent function of thi

Describe the transformations (from the parent function) of this exponential function: y = 3(2^x-1) + 1

Solution

The basic exponential function of this given function is = 2^x

Step 1:

f1(x) = 2^x

f2(x) = 2^(x - 1)

from f1 to f2, graph will move in right direction with 1 unit, without any vertical change

Step 2:

f3(x) = 3*2^(x - 1)

from f2 to f3, in this case graph will vertically stretch three times, without any shift in any direction.

Step 3:

f4(x) = 3*2^(x - 1) + 1

from f3 to f4, graph will vertically shift 1 unit in upward direction, without any horizontal change.

Let me know if you have any doubt.