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

$f(x)=\left(\dfrac{1}{4}\right)^x$

To find:

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

Solution:

We have,

$f(x)=\left(\dfrac{1}{4}\right)^x$

For x=1,

$f(1)=\left(\dfrac{1}{4}\right)^1$

$f(1)=\dfrac{1}{4}\neq 4$

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

For x=-1,

$f(-1)=\left(\dfrac{1}{4}\right)^{-1}$

$f(-1)=4$

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

For x=3,

$f(3)=\left(\dfrac{1}{4}\right)^{3}$

$f(3)=\dfrac{1}{64}$

So, the point $\left(3,\dfrac{1}{64}\right)$ lies on the function f(x).

For x=0,

$f(0)=\left(\dfrac{1}{4}\right)^0$

$f(0)=1$

So, the point $\left(0,\dfrac{1}{4}\right)$ does not lies on the function f(x).

Therefore, the correct options are B and C.