Question

In an exponential function, a horizontal shift goes in the opposite direction; e.g. y=3^(x-4), shift to the right 4. Anyone know why that is? Thanks!

Answer 1

It is true for ALL functions not just exponential functions.

If y = f(x)
y = f(x-4) shifts the function to the RIGHT by 4 units.
y = f(x+4) shifts the function to the LEFT by 4 units.

Answer 2

what is shifting in \(f(x-4)\) is actually the x axis shifts to the left by 4 making the graph appear to shift to the right

Answer 3

Is it possible that I could see a graph of it? Thanks!

Answer 4

If you take f(x) = x^2. When x = 0, y = 0
f(x-4) = (x-4)^2, Now x = 4 makes y = 0. The graph has shifted RIGHT by 4 units.
f(x+4) = (x+4)^2, Now x = -4 makes y = 0. The graph has shifted LEFT by 4 units.