Question

The table below shows the values for the function y= f(x)

Answer 1

Hello!

The answers are:

Second option, evaluating x=-1

$g(-1)=-2$

Fifth option, evaluating x=6

$g(6)=\frac{3}{2}$

Why?

We are given a table that shows the values for the given function (f(x), and we are asked to find the solution of an equivalent function (g(x)).

We have that:

$g(x)=\frac{1}{2}f(x)$

Now, evaluating we have:

For x=-3

$g(-3)=\frac{1}{2}f(-3)=\frac{1}{2}*5=2.5$

We have the values (-3,2.5) so,  it's not part of the solutions to the  function g(x).

For x=-1

$g(-1)=\frac{1}{2}f(-3)=\frac{1}{2}*-4=-2$

We have the values (-1,-2) so,  it's part of the solutions to the function g(x).

For x=0

$g(0)=\frac{1}{2}f(0)=\frac{1}{2}*2=1$

We have the values (0,1) so, it's not part of the solutions to the function g(x).

For x=5

$g(5)=\frac{1}{2}f(5)=\frac{1}{2}*-8=-4$

We have the values (5,-8) so, it's not part of the solutions to the function g(x).

For x=6

$g(6)=\frac{1}{2}f(6)=\frac{1}{2}*3=\frac{3}{2}$

We have the values $(6,\frac{3}{2})$ so, it's part of the solutions to the function g(x).

Hence, we have that the answers are:

Second option, evaluating x=-1

$g(-1)=-2$

Fifth option, evaluating x=6

$g(6)=\frac{3}{2}$

Have a nice day!