Question

Which points are on the graph of g(x) = (1/5)x?

Select each correct answer.
(3, 125) (-2,5) (1, 0) (-1, 5)?

Answer 1

Given:

The function is

`g(x)=((1)/(5))^x`

To find:

The correct ordered pairs.

Solution:

We have,

`g(x)=((1)/(5))^x`

For x=3,

`g(3)=((1)/(5))^3`

`g(3)=(1)/(125)`

So, the ordered pair is
`(3,(1)/(125))`.

For x=-2,

`g(-2)=((1)/(5))^(-2)`

`g(-2)=(5)^2`
`[\because ((a)/(b))^(-n)=((b)/(a))^n]`

`g(-2)=25`

So, the ordered pair is
`(-2,25)`.

For x=1,

`g(1)=((1)/(5))^1`

`g(1)=(1)/(5)`

So, the ordered pair is
`(1,(1)/(5))`.

For x=-1,

`g(-1)=((1)/(5))^(-1)`

`g(-1)=(5)^1`
`[\because ((a)/(b))^(-n)=((b)/(a))^n]`

`g(-1)=5`

So, the ordered pair is (-1,5). This is the correct answer.

Therefore, the correct option is D.