Given the function:
[tex]y=-4\cdot3^x[/tex]
One of the following choices is false:
a. The function decreases.
The function
[tex]y=3^x[/tex]
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:
[tex]\begin{gathered} y=-4\cdot3^0 \\ y=-4\cdot1=-4 \end{gathered}[/tex]
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:
[tex]\begin{gathered} y=-4\cdot3^3 \\ y=-4\cdot27 \\ y=-108 \end{gathered}[/tex]
The new point is (3, -108). It's evident that -108 is not the triple of -4, thus this statement is false.
Answer: C
