Chapter 4.6, Problem 50E

To determine

To explain: whether the statement of friend is correct or not

Answer to Problem 50E

The statement of friend is friend is correct.

Explanation of Solution

Calculation:

Consider that your friend says that the range of a function that represents an arithmetic sequence always contains only positive numbers or only negative numbers and he claims this is because the domain is set of positive integers and the output values either constantly increase or constantly decrease.

The arithmetic sequence's domain consists of the natural numbers $\{1,2,3,\mathrm{...}),$ and the range consists of the terms of the sequence. So, the graph will be in the first quadrant if the sequence terms are positive and will be in fourth quadrant if the sequence terms are negative.

Conclusion:

Therefore, the statement of friend is friend is correct.