Question

Which function is a shrink of the exponential growth function shown on the graph?

A) f(x) = 2(3)^x

B) f(x) = 1/2(3)^x

C) f(x) = 2(1/3)^x

D) f(x) = 1/2(1/3)^x

Answer 1

For exponential functions
y=ab^x,
where
a is the scale vertical stretch factor,
b is the base, and
x the exponent (also independent variable)

It is a know fact that if the scale factor (1/2 or 2 in the answer choices) is positive, the graph is increasing if the base (3 or 1/3) is greater than 1.
This means that the base cannot be equal to 1/3. This eliminates choices 3 and 4.

Next, for a base greater than 1 (3>1), and the scale factor positive, it is a dilation (image gets bigger) if the scale factor is greater than 1. This eliminates the first choice where a=2.

This leaves us with the second choice where a=1/2, b=3, which is a shrink of the given exponential base function.

Answer 2

Answer:the answer is b

Explanation:

just took the test and got it right.