Question

chorus is selling christmas ornaments. they bought a box of 250 ornaments. they sell the ornaments for $15 each. let x be the number of ornaments and y be the amount of money made for the function y = 15x. what is the domain and range in context to the problem?

Explanation:

Step1: Determine the domain

They have 250 ornaments to sell, so the number of ornaments sold \(x\) is a non - negative integer and \(0\leq x\leq250\). Since \(x\) represents the number of ornaments and can only take on whole number values, the domain is discrete. The domain is the set of all non - negative integers \(x\) such that \(0\leq x\leq250\), written in set - builder notation as \(\{x\in\mathbb{Z}:0\leq x\leq250\}\).

Step2: Determine the range

We know that \(y = 15x\). When \(x = 0\), \(y=0\); when \(x = 250\), \(y=15\times250 = 3750\). Since \(x\) is a non - negative integer, \(y\) will also be a non - negative multiple of 15. The range is the set of all non - negative multiples of 15 such that \(0\leq y\leq3750\), written in set - builder notation as \(\{y\in\mathbb{Z}:y = 15x,0\leq x\leq250\}\) and it is also discrete.

Answer:

Domain: The set of non - negative integers \(x\) where \(0\leq x\leq250\) (discrete). Range: The set of non - negative multiples of 15 where \(0\leq y\leq3750\) (discrete).