Question

The graph shows the function f(x) = (2.5)x was horizontally translated left by a value of h to get the function g(x) = (2.5)x–h.

On a coordinate plane, 2 exponential functions are shown. f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.5) and crosses the y-axis at (0, 1). g (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 2, 1) and crosses the y-axis at (0, 6).
What is the value of h?

–2
0
2
5

Answer 1

Answer: 2

Reason: From f(-1)=0.5 and f(0)=1 we get f(x)=2^x. A left shift by h gives g(x)=f(x+h)=2^{x+h}. Using g(-2)=1: 2^{h-2}=1 so h-2=0 and h=2.