Question

Which of the following is false about the function y=-4*3^x?

Answer 1

Given the function:

`y=-4\cdot3^x`

One of the following choices is false:

a. The function decreases.

The function

`y=3^x`

is strictly increasing in all of its domain. Our function is -4 times that function, so it decreases in all of its domain.

This statement is true

b. The function has a y-intercept of (0, -4)

Substituting x = 0:

`\begin{gathered} y=-4\cdot3^0 \\ y=-4\cdot1=-4 \end{gathered}`

This statement is also true

c. If the value of x increases by 3, the value of y will triple.

We have already found the point (0, -4). Let's increase x by 3 by setting x = 3:

`\begin{gathered} y=-4\cdot3^3 \\ y=-4\cdot27 \\ y=-108 \end{gathered}`

The new point is (3, -108). It's evident that -108 is not the triple of -4, thus this statement is false.

Answer: C