Question

The graph shows that is translated horizontally and vertically to create the function .

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 = 2 in quadrant 2 and increases into quadrant 1. It goes through (0, 2) and (2, 3).

What is the value of h?

−2
−1
1
2

Answer 1

f(x)=2^x (since f(0)=1 and f(−1)=0.5). A horizontal shift h and a vertical shift up 2 gives
g(x)=2^{\,x−h}+2.
Using the point (2,3): 2^{2−h}+2=3 ⇒ 2^{2−h}=1 ⇒ 2−h=0 ⇒ h=2.

Answer: 2