Respuesta :

To see what function corresponds to the table we can start by trial and error.

But we can have a hint to make it easier. We know that a number to the power of 0 will be 1. The table shows that, when x (the expoonent) is 0, we obtain a value of y = 6. This means that in the function, the number that has the x exponent should be multiplied by 6, so when it is to the power of 0 we obtain:

[tex]6\cdot(n)^0=6\cdot1=6[/tex]

With n being any number.

With this we can say that the correct answer is the third option. Let's prove it:

When x = -1, y = 12:

[tex]y=6\cdot(\frac{1}{2})^{-1}=6\cdot(\frac{2}{1})^1=6\cdot2=12^{}[/tex]

When x = 0, y = 6:

[tex]y=6\cdot(\frac{1}{2})^0=6\cdot1=6[/tex]

When x = 1, y = 3:

[tex]y=6\cdot(\frac{1}{2})^1=6\cdot\frac{1}{2}=\frac{6}{2}=3[/tex]

When x = 2, y = 3/2:

[tex]y=6\cdot(\frac{1}{2})^2=6\cdot\frac{1^2}{2^2}=6\cdot\frac{1}{4}=\frac{6}{4}=\frac{3}{2}[/tex]

This proves the correct answer is the third option. It satisfied each point of the table.