Jerry charges $15 for each lawn that he cuts. His earnings vary from week to week. If he cuts at most 10 yards per week, his profit is represented by y = 15x - 10 because he allows $10 for gas and oil for his equipment. What do the domain values represent on the graph? Which domain values are significant in this problem?
A) profit on each yard; x < 18
B) number of yards Jerry cuts; x ≥ 0
C) number of yards Jerry cuts; x ≥ 10
D) number of yards Jerry cuts; 0 ≤ x ≤ 10
It's D.
You said:
"...he cuts at most 10 yards per week..."
The domain values on the graph represent the variable for the number of yards Jerry cuts. In this problem, the domain values are the x-values, which represent the number of yards Jerry cuts.
From the answer choices provided, option B) "number of yards Jerry cuts; x ≥ 0" is the correct interpretation of the domain values in this problem. The number of yards Jerry cuts can be any non-negative value (greater than or equal to 0), as it makes sense in the context of the problem. Jerry may cut 0 yards in a week, meaning he doesn't cut any lawns that week, or he may cut multiple lawns.
Option C) "number of yards Jerry cuts; x ≥ 10" is also a possible interpretation of the domain values, but it is not the significant interpretation in this problem. It suggests that Jerry only cuts lawns if the number of yards is greater than or equal to 10, which is not mentioned in the problem statement.
Option D) "number of yards Jerry cuts; 0 ≤ x ≤ 10" restricts the number of yards to be between 0 and 10, which is also not mentioned in the problem statement. Hence, it is not the correct interpretation.
Option A) "profit on each yard; x < 18" is not the correct interpretation of the domain values. The domain values are referring to the number of yards (x) and not the profit on each yard.
So, the correct interpretation of the domain values is option B) "number of yards Jerry cuts; x ≥ 0".