The graph of a function f (x) is translated 3 units up and 2 units left. Write the transformed function g(x) in terms of the original function f (x):

Answer 1

Hello Samrah,

You're shifting the original function f(x) 2 units LEFT. Horizontal shifts are taken care of in the parentheses, and going 2 left means you ADD 2 in the parentheses. So you now have f(x+2)

Next, you translate f(x) 3 units up. So you ADD 3 to where you currently are. As a result: f(x+2) + 3

So the transformed function can be expressed as: g(x) = f(x+2) + 3

Cheers!