List the transformations occurring to the parent function f(x)=2^x in g(x)=4×2^x-5

Answer 1

When I look at your question, the first thing I do is try to write g(x) in terms of f(x).

g(x) = 4 * [ 2^x ] - 5

g(x) = 4* [ f(x) ] - 5

With f(x) found, I can determine which transformations happened.

Answer 2

The 4 is a vertical stretch by a factor of 4.

For the -5, it depends if this is a part of the exponent or not.

If the -5 is in the exponent, it is a horizontal shift by 5 units to the right.

If it is not, it is a vertical shift down 5 units.