Question

he graphs of f(x) = 10x and its translation, g(x), are shown.

On a coordinate plane, 2 exponential functions are shown. f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 1) and goes through (1, 10) and (2, 100). g (x) approaches y = 0 in quadrant 2 and increases into quadrant 2. It goes through (3, 1), (4, 10), and (5, 100).
What is the equation of g(x)?

g(x) = 10x – 3
g(x) = 10x + 3
g(x) = 10x – 3
g(x) = 10x + 3

Answer 1

g(x) = 10^(x−3)

Explanation: g(x) is f(x) shifted right 3 units. So replace x by x−3: g(x)=10^{x−3}. Check: g(3)=10^0=1, g(4)=10^1=10, g(5)=10^2=100.