Question

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

Table:
X Y
-3 5
-1 -4
0 2
5 -8
6 3

If g(x)=1/2f(x), which of the following are solutions to g(x)
(-3,5.5)
(-1,-2)
(0,4)
(5,-8)
(6,3/2)

Answer 1

(-1,-2) and (6, 3/2)

Explanation:

Have a good day :)

Answer 2

Hello!

The answers are:

Second option, evaluating x=-1

`g(-1)=-2`

Fifth option, evaluating x=6

`g(6)=(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)=(1)/(2)f(x)`

Now, evaluating we have:

For x=-3

`g(-3)=(1)/(2)f(-3)=(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)=(1)/(2)f(-3)=(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)=(1)/(2)f(0)=(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)=(1)/(2)f(5)=(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)=(1)/(2)f(6)=(1)/(2)*3=(3)/(2)`

We have the values
`(6,(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)=(3)/(2)`

Have a nice day!