Question

Which of the following exponential functions is represented by the data in the table?Question 12 options:A) ƒ(x) = x3B) ƒ(x) = 3xC) ƒ(x) = (1∕3)xD) ƒ(x) = x1∕3

Answer 1

C.

`f(x)=((1)/(3))^x`

Step-by-step explanation:

Given:

To find:

The exponential function represented by the data in the given table

Let's go ahead and check each of the given functions to determine the right function;

*For the first function;

`\begin{gathered} f(x)=x^3 \\ f(-3)=(-3)^3=-27 \end{gathered}`

We can see that the first function is not the right function

*For the second function:

`\begin{gathered} f(x)=3^x \\ f(-3)=3^(-3)=(1)/(27) \end{gathered}`

We can see that the first function is not the right function

*For the third function:

`\begin{gathered} f(x)=((1)/(3))^x \\ f(-3)=((1)/(3))^(-3)=27 \\ f(-2)=((1)/(3))^(-2)=9 \\ f(-1)=((1)/(3))^(-1)=3 \\ f(0)=((1)/(3))^0=1 \\ f(1)=((1)/(3))^1=(1)/(3) \\ f(2)=((1)/(3))^2=(1)/(9) \\ f(3)=((1)/(3))^3=(1)/(27) \end{gathered}`

We can see that the third function is the right function