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

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

When x = -2

$f(-2)=3\left(\frac{1}{4}\right)^{-2} \\ \\ =3(4)^2=3(16)=48$

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

When x = 0

$f(0)=3\left(\frac{1}{4}\right)^{0} \\ \\ =3(1)=3$

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

When x = 2

$f(2)=3\left(\frac{1}{4}\right)^{2} \\ \\ =3\left(\frac{1}{16}\right)=\frac{3}{16}$

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

When x = 12

$f(12)=3\left(\frac{1}{4}\right)^{12} \\ \\ =3\left(\frac{1}{16777216}\right)=\frac{3}{16777216}\approx0$

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