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\}`

Step-by-step 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\}`