Question

Given the sequence 2, 4, 8, , 16,........, where x = 0, 1, 2, 3, .......what is the function rule? f(x) = 2x + 2 f(x) = 2(2)x f(x) = (2x) f(x) = 2

Answer 1

Option C: $f(x)=2^x$ is the function rule.

Explanation:

The sequence is $2,4,8,16, \dots \dots$

Let us find the common difference of this sequence.

Common ratio = $\frac{4}{2} =2$

Hence, $r=2$

Thus, the given sequence is a geometric progression.

To determine the function rule, let us substitute the values in the general formula of GP which is given by

$f(x)=ar^{x-1}$ where $a=2, r=2$

Substituting we get,

$f(x)=2(2)^{x-1}$

Simplifying, we get,

$f(x)=2\times2^x\times2^{-1$

Adding the powers, we get,

$f(x)=2^{1+x-1}$

Simplifying, we get,

$f(x)=2^x$

Hence, the function rule is $f(x)=2^x$

Thus, Option C is the correct answer.