Determine the function that represents the transformed graph

Determine the function that represents the transformed graph of f(x) = 2^x.

Solution

f(x) = 2^x

g(x) passes through (-2,-4) , (0,-7)

graph of f(x) is 6 units downwards shifted

horizontal shift of 2 units to the left, so h = -2

it is reflected across x axis so, a =-1

so the function becomes

y = -2 ^ (x+2) - 3