Trasformatons (2)

Question

Which function represents a horizontal shift of ƒ(x) = 5^x by 4 units to the right?

g(x) = 5^x + 4

g(x) = 5^{(x - 4)}

g(x) = 5^x - 4

g(x) = 9^x

Answer 1

Transformations of f(x) = 5^x:

g(x) = a·5^b(x-c) + d

1. a = vertical stretch factor = 1 if no stretch
2. b = horizontal compression factor = 1 if no compression
3. c = horizontal shift: c > 0 right, c < 0 left, c = 0 if no left/right shift
4. d = vertical (up/down) shift: d > 0 is up, d < 0 is down, d = 0 if no up/down shift

All you have is a horizontal shift by 4 units to the right, so a = 1, b = 1, c = 4, d = 0. Plug those numbers into the g(x) formula above and simplify to get the answer. Post your answer as a comment and I (or another tutor) will verify it for you.