Question

which is a shrink of an exponential growth function? a. f(x) = 1/3(3)^x b. f(x) = 3(3)^x c. f(x) = 1/3(1/3)^x d. f(x) = 3(1/3)^x

Answer 1

Answer: option a.

$f(x)=\frac{1}{3} (3)^x$

Explanation:

A shrink of a function is a shrink on the vertical direction. It means that for a certain value of x, the new function will have a lower value, in the intervals where the function is positive, or a higher value, in those intervals where the function is negative. This is, the image of the new function is shortened in the vertical direction.

That is the reason behind the rule:

• given f(x), the graph of the function a×f(x), when a > 1, represents a vertical stretch of f(x),

• given f(x), the graph of the function a×f(x), when a < 1, represents a vertical shrink of f(x).

So, we just must apply the rule: to find a shrink of an exponential growth function, multiply the original function by a scale factor less than 1.

Since it is a shrink of an exponential growth function, the base must be greater than 1. Among the options, the functions that meet that conditon are a and b:

$a. f(x)=\frac{1}{3} (3)^x \\ \\ b.f(x) = 3(3)^x$

Now, following the rule it is the function with the fraction (1/3) in front of the exponential part which represents a shrink of an exponential function.

Answer 2

Shrink of an exponential growth function is f(x) = 1/3(3)^x