Let's carefully analyze and interpret the given statements and features about Jada's profit situation:
1. [tex]$y$[/tex]-intercept: The [tex]$y$[/tex]-intercept of a function typically represents the value of the function when the independent variable (in this case, the number of kilograms of paprika sold) is zero. The given statement associated with the [tex]$y$[/tex]-intercept is:
> "If Jada doesn't sell anything, she loses \[tex]$250."
This means that when Jada sells 0 kilograms of paprika, her profit (or loss) is -\$[/tex]250. Thus, the [tex]$y$[/tex]-intercept of the profit function is -250.
2. Positive or negative interval: This feature concerns the intervals over which the function is positive (indicating profit) or negative (indicating loss). The statement provided is:
> "Jada needs to sell more than 35 kilograms in order to make a profit."
This statement indicates that for profit to be positive, Jada must sell more than 35 kilograms of paprika. Therefore, the profit function is negative when she sells 35 kilograms or fewer.
3. Increasing interval: This feature describes the behavior of the function as Jada sells more paprika:
> "The more paprika Jada sells, the more profit she makes."
This suggests that the profit function is increasing as the quantity of paprika sold increases.
To summarize, we have the following insights:
- The [tex]$y$[/tex]-intercept of the profit function is -250.
- Jada makes a profit if she sells more than 35 kilograms of paprika.
- The profit function increases as the amount of paprika sold increases.
By understanding these features and statements, we can form a clear picture of the relationship between the amount of paprika Jada sells and her resulting profit.
