Question

Is the function f(x)=-(4/3)^(-6x) an exponential function? If so identify the base. If not, why not?

Answer 1

It may be easier for you to answer this question if you'd consider f(x)=(4/3)^(-6x) first. Is this an exponential function? Why or why not?

Answer 2

Is\[(\frac{ 4 }{ 3 })^{-6x}\]

Answer 3

an exponential function?

Answer 4

I don't think so because it is greater than one and negative.

Answer 5

Well greater than -1 that is

Answer 6

What are you refering to when you use the pronoun "it?" Unclear.

What does an "exponential function" look like, according to what you already know?

Answer 7

The base is "it", my bad sorry.

Answer 8

Exponential function: f(x)=b^x, b>0, b is not equal to 1.

Answer 9

In this particular problem, what is the base?

Answer 10

Thanks for looking up "exponential function." Good move!

Answer 11

The base here is -(4/3) however I don't think this is right because it doesn't follow the guidelines

Answer 12

Of course, thank you as well for helping!

Answer 13

Ignore the ' - ' sign for now. Focus on the quantity inside parentheses.

Again: What is the base here?

Answer 14

In that case it is 4/3

Answer 15

Wait
no

Answer 16

one moment please

Answer 17

In what instances would I find the reciprocal? Because it might then be 3/4^6

Answer 18

I just wanted you to identify the base here. It's (4/3). Does that "meet the guidelines?"

Answer 19

no

Answer 20

Actually, it does. Why do you believe it does not satisfy the guidelines?

Answer 21

I thought it didn't because 4/3 is equal to 1.3333 so it is not less than 1

Answer 22

The rules state that the base cannot be 0 or smaller, and cannot be 1, but any other quantity is acceptable as a base.

Answer 23

4/3 can definitely be a base, since it is positive and is not = to 1.

Answer 24

Oh! You're right

Answer 25

What about the negative though?

Answer 26

Put the neg sign back in only after you've decided whether (4/3)^(-6x) is or is not an expo. function.

If y ou were to graph both versions, you'd see that one is the reflection of the graph of the other in the x-axis. Both are expo. functions.

Answer 27

Caution: It's -(4/3), not (-4/3).

Answer 28

Ah okay, I will keep that in mind!

Answer 29

However, my answer should be (3/4)^6 as the base. I finished the lesson, and got the right answer but don't understand the conversion from -(4/3) to that.

Answer 30

I asked you to take out the - sign because (in the original problem) it has NO bearing on whether or not the given function is an expo function.

all you were asked to do was to identify the base and determine whether or not the function is expo or not.

The base is (4/3), not (4/3)^6, at least to my way of thinking. However, you are correct technically:

[(4/3)^(-6)]^x can be simplified and results in a function whose exponent is simply x, not -6x.