Question

Determine which ordered pair(s) lie on the function f(x)=(1/4)^x. (1,4) (-1,4), (3, 1/64), (0, 1/4)

Answer 1

Given:

The function is

`f(x)=\left((1)/(4)\right)^x`

To find:

The ordered pair(s) from the options lie on the function.

Solution:

We have,

`f(x)=\left((1)/(4)\right)^x`

For x=1,

`f(1)=\left((1)/(4)\right)^1`

`f(1)=(1)/(4)\\eq 4`

So, the point (1,4) does not lies on the function f(x).

For x=-1,

`f(-1)=\left((1)/(4)\right)^(-1)`

`f(-1)=4`

So, the point (-1,4) lies on the function f(x).

For x=3,

`f(3)=\left((1)/(4)\right)^(3)`

`f(3)=(1)/(64)`

So, the point
`\left(3,(1)/(64)\right)` lies on the function f(x).

For x=0,

`f(0)=\left((1)/(4)\right)^0`

`f(0)=1`

So, the point
`\left(0,(1)/(4)\right)` does not lies on the function f(x).

Therefore, the correct options are B and C.