Question

Which ordered pairs lie on the graph of the exponential function f(x)=3(1/4)x?

Select each correct answer.

​ (−2,48) ​

​ (0,3) ​

​ (2,3/16) ​

​ (12,0) ​

Answer 1

Given the function


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

When x = -2


`f(-2)=3\left((1)/(4)\right)^(-2) \\ \\ =3(4)^2=3(16)=48`

Thus, (-2, 48) lies on the graph of the given function.

When x = 0


`f(0)=3\left((1)/(4)\right)^(0) \\ \\ =3(1)=3`

Thus, (0, 3) lies on the graph of the given function.

When x = 2


`f(2)=3\left((1)/(4)\right)^(2) \\ \\ =3\left((1)/(16)\right)=(3)/(16)`

Thus, (2, 3/16) lies on the graph of the given function.

When x = 12


`f(12)=3\left((1)/(4)\right)^(12) \\ \\ =3\left((1)/(16777216)\right)=(3)/(16777216)\approx0`

Thus, (12, 0) lies on the graph of the given function.