Chapter 1.6, Problem 39HP

To determine

To describe: A real-world situation where it is possible to have a negative number included in domain in range.

Answer to Problem 39HP

The domain and range can both be negative in below described real-life situation concerning dieting competition.

Explanation of Solution

Given information: Negative number should be included in domain or range.

Think about a situation in which a dieting competition is carried out, all the participants have $\$1000$ at the start of the game, duration of the competition is $30$ days. Every day every participant is weighed, if the weight turns out to be more than the weight on day $1$ , then the points are deducted from the participant’s account and if weight is less, then point are added to the account. The competitor having highest number of points at the end of competition is declared winner.

Function is $f(x)=B-\left(\frac{x}{2}\right)$

where $B$ is initial account balance, $x$ represents change in weight (in grams).

Change in weight $x$ and $f(x)$ (Final balance on day-to-day basis) can both be negative.

Thus, domain and range can both be negative in above described real-world situation.