Lucy needs to buy some organic apples, and her grocery store is having a sale on them. If she buys 3 or fewer pounds of apples, the price will be $1.50 per pound. If she buys more than 3 pounds of apples, the price is $1.10 per pound. What is the domain of the piecewise-defined function, where $x$ represents the number of pounds of apples?
A. {x | x ≥ 0}
B. {x | x is a real number}
C. {x | 0 ≤ x ≤ 3}
D. {x | x ≥ 3}
Answer (2)
The number of pounds of apples Lucy buys must be non-negative.
The domain is all non-negative real numbers.
The domain is represented by the inequality x ≥ 0 .
The final answer is x ∣ x ≥ 0
Explanation
Understanding the Problem The problem asks for the domain of a piecewise-defined function representing the number of pounds of apples Lucy buys. The number of pounds of apples must be non-negative since Lucy cannot buy a negative amount of apples. Therefore, the domain includes all real numbers greater than or equal to 0.
Determining the Domain The domain of the function is the set of all possible values of x , where x represents the number of pounds of apples. Since Lucy can buy any non-negative amount of apples, the domain is all real numbers greater than or equal to 0. This can be written as x ≥ 0 .
Final Answer The domain of the piecewise-defined function is the set of all non-negative real numbers. This is represented by the inequality x ≥ 0 . Therefore, the correct answer is: x ∣ x ≥ 0
Examples
Understanding the domain of a function is crucial in many real-world scenarios. For instance, if you're calculating the cost of materials for a project, the quantity of materials cannot be negative. Similarly, when modeling population growth, time cannot be negative. In these cases, the domain of the function is restricted to non-negative values, ensuring that the model reflects realistic constraints.
The domain of the piecewise-defined function is all non-negative real numbers, represented by the inequality x ≥ 0 . The correct answer choice is (A) {x | x ≥ 0}. This indicates that Lucy can buy 0 or more pounds of apples freely.
;
