Question

The table shown gives values of the function y=g(x) for selected values of x. Which represents g(x)

Answer 1

Given:

A table with the given values of the function y=g(x).

To find the function that represents g(x), we substitute a value of x into the given options.

For:

g(x =3+2x:,:

Let x=3

`\begin{gathered} g(x)=3+2x \\ =3+2(3) \\ =9 \end{gathered}`

Based on the given table, the value g(x) is 24 when x=3. So g(x)=3+2x is not the function that represents g(x).

For

`\begin{gathered} g(x)=3\cdot2x \\ =3\cdot2(3) \\ =18 \end{gathered}`

The value of g(x) =18 when x=3, so this is not the function.

For g(x)=3x^2:

`\begin{gathered} g(x)=3x^2 \\ =3(3)^2 \\ =27 \end{gathered}`

Hence, this is not the function as well.

For g(x)=3(2)^x:

`\begin{gathered} g(x)=3\cdot2^x \\ =3\cdot2^3 \\ =3(8) \\ g(x)=24 \end{gathered}`

We can notice that when x=3, the value of g(x) =24 which is the same as the value of g(x) in the given table.

To double check this, we plug in the other values of x.

Therefore, the answer is:

`g(x)=3\cdot2^x`