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

By definition, we have to:

An arithmetic sequence is a sequence of numbers that increases or decreases by a constant amount each term.

We can write a formula for the term n of an arithmetic sequence in the form:

an = d * n + c

Where,

n: domain variable

c: initial value

d: constant term.

For this case we have:

an = 4 * n + c

Answer:

The function f (x) is an arithmetic sequence.

Answer 2

Option 1 is correct that is the function f(x) is an arithmetic sequence.

Explanation:

We have been given the information that function is increasing by 4 for every unit in the domain.

That means difference between the consecutive terms will be same that is common difference exists

For example:

we have a function f(x)=x

Since, it is increasing by 4 for every unit means function becomes x,x+4,x+4+4

The common difference is 4.

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

therefore, option 1 is correct.