Question

A graph of f(x)=2^x is shifted up 3 units, and then shifted left 2 units

Write the transformed function

Answer 1

Shift up 3 units: f(x) + 3
Shift left 2 units: f(x + 2)
Therefore, the transformed function is:
g(x) = f(x + 2) + 3
Substituting f(x) = 2^x, we get:
g(x) = 2^(x + 2) + 3
Simplifying, we get:
g(x) = 2^x * 2^2 + 3
g(x) = 4 * 2^x + 3
Therefore, the transformed function is g(x) = 4 * 2^x + 3.