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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

Which Of The Following Exponential Functions Is Represented By The Data In The TableQuestion 12 OptionsA Ƒx X3B Ƒx 3xC Ƒx 13xD Ƒx X13 class=
Which Of The Following Exponential Functions Is Represented By The Data In The TableQuestion 12 OptionsA Ƒx X3B Ƒx 3xC Ƒx 13xD Ƒx X13 class=

Sagot :

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

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