Question

Melinda has shown that a function, f(x), increases by 4 for every unit in the domain. What does this prove?

The function f(x) is an arithmetic sequence.
The function f(x) is a geometric sequence.
The function f(x) is not a sequence.
This does not prove anything.

Answer 1

Answer:-The function f(x) is an arithmetic sequence.

Explanation:-

Let
`a_1` be the initial value

According to the question

`a_2=a_1+4`

`a_3=a_2+4\\\Rightarrow\ a_3=(a_1+4)+4\\\Rightarrow\ a_3=a_1+4+4\\\Rightarrow\ a_3=a_1+2(4)\\\Rightarrow\ a_3=a_1+2*4\\\Rightarrow\ a_3=a_1+(3-1)4` and so on

Thus, we can write a formula for the term n of an arithmetic sequence in the form:

`a_n=a_1+(n-1)4`

where, n=1,2,3,4,....

4= common difference

Therefore, the function f(x) is an arithmetic sequence.

• An arithmetic sequence is a sequence of numbers in which each term increases or decreases by a constant number.