1
advanced-math

The function f(x)=8(2)xf(x) = 8(2)^x is transformed to g(x)=8(2)x3g(x) = 8(2)^{x-3}. How does the graph shift?

A

3 units right

B

3 units left

C

3 units up

D

3 units down

Correct Answer: A

Choice A is the correct answer. Identify the horizontal shift.

  1. Form: y=a(b)xhy = a(b)^{x-h} shifts right by hh units.
  2. Given: g(x)=8(2)x3g(x) = 8(2)^{x-3}, so h=3h = 3.
  3. Shift: Graph moves 3 units to the right.

💡 Strategic Tip:(xh)(x - h) shifts right, (x+h)(x + h) shifts left.

Choice B is incorrect because(x3)(x - 3) means right, not left. Choice C is incorrect because this would require adding a constant outside. Choice D is incorrect because vertical shifts involve adding/subtracting from the entire function.