Mrs. Dizeu had a summer job that pays $15.00 an hour and she worked between 10 and 40 hours every week. Her weekly salary can be modeled by the equation: S = 15h, where S is her weekly salary and h is the number of hours she worked in a week. Describe the domain and range for this problem using interval notation.

The domain of the function regarding Mrs. Dizeu’s summer job relates to the independent variable, which in this case is the number of hours (h) she worked every week. Since the problem states that she worked between 10 and 40 hours every week, the domain is the set of hours from 10 to 40, inclusive. In interval notation, the domain is written as [10, 40].

The range of the function concerns the dependent variable, which in this case is her weekly salary (S). Given that her hourly pay is $15.00 per hour, the smallest amount she can earn in a week (if she works the minimum 10 hours) is 15 * 10 = $150, and the largest amount she can earn in a week (if she works the maximum 40 hours) is 15 * 40 = $600. Therefore, the range of her weekly salary is from $150 to $600, inclusive. In interval notation, the range is written as [150, 600].

Extra: Domain and Range concepts: - The domain of a function is the complete set of possible values of the independent variable. In simpler terms, it's all the values that you can put into a function and get a valid output. In this job salary problem, the number of hours Mrs. Dizeu can work is limited by the conditions of her employment, which specify a lower bound (10 hours) and an upper bound (40 hours).

- The range of a function is the complete set of possible values of the dependent variable, which result from using the function. This is the output of the function for all the inputs within the domain. In this case, Mrs. Dizeu's weekly salary is dependent on the number of hours she works. If she works more hours, her salary increases.

Interval Notation is a way of writing subsets of the real number line. An interval notation includes: - Square brackets [ ] which denote inclusive boundaries, meaning the endpoints are included in the set. - Parentheses ( ) which denote exclusive boundaries, meaning the endpoints are not included in the set.

In the case of Mrs. Dizeu's job, since she can work exactly 10 or 40 hours and can earn exactly $150 or $600, we use square brackets to show that these values are included in the domain and range. If, for some reason, she could work more than 10 but less than 40 hours, the domain would be written with parentheses: (10, 40). Similarly, if she could earn more than $150 but less than $600, the range would be written with parentheses: (150, 600). Since that's not the case here, we use square brackets for both the domain [10, 40] and the range [150, 600].