Question

select the correct answer.
the postal service charges $2 to ship packages up to 5 ounces in weight, and $0.20 for each additional ounce up to 20 ounces. after that, they charge $0.15 for each additional ounce.
what is the domain of this relation?
graph with x-axis: weight (ounces) from 0 to 50, y-axis: cost (dollars) from 0 to 10. a line starts at (0,2), horizontal to (5,2), then increasing. below the graph: options a. 2 ≤ x ≤ 9.5; b. x ≤ 50; c. x ≥ 2; d. x ≥ 0

Explanation:

Step1: Understand the domain concept

The domain of a relation (in this context, the function relating weight to cost) is the set of all possible input values (here, weight in ounces, \( x \)).

Step2: Analyze the graph and context

• The \( x \)-axis (weight) in the graph goes from 0 to 50 ounces.
• The postal service's charging structure is for packages, so weight can't be negative (since you can't have a negative - weight package), but the graph's \( x \)-axis ends at 50, and the context implies the weight considered here is up to 50 ounces (as seen from the graph's \( x \)-scale).
• Option A is about cost (\( y \)-values, range), not domain.
• Option C is about cost (\( y \geq 2 \), range).
• Option D suggests \( x \geq 0 \), but the graph and context show the weight considered is up to 50 (since the \( x \)-axis is labeled up to 50, and the charging structure's graph is plotted up to 50 ounces). So the domain is \( x \leq 50 \) (since weight can be from 0 up to 50 ounces, and \( x \leq 50 \) includes non - negative weights up to 50).

Answer:

B. \( x \leq 50 \)