Question

4,12,36,108,324
If the sequence defines a function, what is a reasonable domain and range of the function?

Answer 1

The sequence defines a function $f(x)=4.(3)^{x-1}$

Domain : $\{1,2,3,4,5\}$

Range : $\{4,12,36,108,324\}$

Explanation:

A sequence defines a function if it is the set of natural numbers.

Thus, the function is given by

$f(x)=4.(3)^{x-1}$

The sequence can be determined by substituting the values for x.

For $x=1$,

$f(1)=4(3)^{0}=4$

For $x=2$,

$f(2)=4(3)^{1}=4(3)=12$

For $x=3$,

$f(3)=4(3)^{2}=4(9)=36$

For $x=4$,

$f(4)=4(3)^{3}=4(27)=108$

For $x=5$,

$f(5)=4(3)^{4}=4(81)=324$

Thus, from these the domain and range of a function can be determined.

The domain of a function is the set of independent values, which are generally the x-coordinates.

Domain of a function is $\{1,2,3,4,5\}$

The range of a function is the set of dependent values obtained by substituting the values for x.

Range of a function is $\{4,12,36,108,324\}$