Question

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

Answer 1

Given:

The function is

$g(x)=(\dfrac{1}{5})^x$

To find:

The correct ordered pairs.

Solution:

We have,

$g(x)=(\dfrac{1}{5})^x$

For x=3,

$g(3)=(\dfrac{1}{5})^3$

$g(3)=\dfrac{1}{125}$

So, the ordered pair is $(3,\dfrac{1}{125})$.

For x=-2,

$g(-2)=(\dfrac{1}{5})^{-2}$

$g(-2)=(5)^2$             $[\because (\dfrac{a}{b})^{-n}=(\dfrac{b}{a})^n]$

$g(-2)=25$

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

For x=1,

$g(1)=(\dfrac{1}{5})^1$

$g(1)=\dfrac{1}{5}$

So, the ordered pair is $(1,\dfrac{1}{5})$.

For x=-1,

$g(-1)=(\dfrac{1}{5})^{-1}$

$g(-1)=(5)^1$             $[\because (\dfrac{a}{b})^{-n}=(\dfrac{b}{a})^n]$

$g(-1)=5$

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

Therefore, the correct option is D.