ANSWER:
C.
[tex]f(x)=(\frac{1}{3})^x[/tex]
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;
[tex]\begin{gathered} f(x)=x^3 \\ f(-3)=(-3)^3=-27 \end{gathered}[/tex]
We can see that the first function is not the right function
*For the second function:
[tex]\begin{gathered} f(x)=3^x \\ f(-3)=3^{-3}=\frac{1}{27} \end{gathered}[/tex]
We can see that the first function is not the right function
*For the third function:
[tex]\begin{gathered} f(x)=(\frac{1}{3})^x \\ f(-3)=(\frac{1}{3})^{-3}=27 \\ f(-2)=(\frac{1}{3})^{-2}=9 \\ f(-1)=(\frac{1}{3})^{-1}=3 \\ f(0)=(\frac{1}{3})^0=1 \\ f(1)=(\frac{1}{3})^1=\frac{1}{3} \\ f(2)=(\frac{1}{3})^2=\frac{1}{9} \\ f(3)=(\frac{1}{3})^3=\frac{1}{27} \end{gathered}[/tex]
We can see that the third function is the right function
