Question

What is the growth factor of f(x) = 3^(x-2)?
A) 3
B) 2
C) 1/3
D) 1/9

Answer 1

The growth factor of f(x) = 3^(x-2) is 3.

Step-by-step explanation:

The growth factor of the function f(x) = 3^(x-2) can be found by comparing the values of f(x) for two different values of x. Let's compare f(x) for x = 0 and x = 1:

For x = 0, f(0) = 3^(0-2) = 3^(-2) = 1/3^2 = 1/9

For x = 1, f(1) = 3^(1-2) = 3^(-1) = 1/3^1 = 1/3

The ratio of f(x) for x = 1 to f(x) for x = 0 is (1/3)/(1/9) = (1/3) * (9/1) = 3/1 = 3

Therefore, the growth factor of f(x) = 3^(x-2) is 3.