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The postal service charges [tex]$\$[/tex]2[tex]$ to ship packages up to 5 ounces in weight, and $[/tex]\[tex]$0.20$[/tex] for each additional ounce up to 20 ounces. After that, they charge [tex]$\$[/tex]0.15[tex]$ for each additional ounce.

What is the domain of this relation?

A. $[/tex]2 \leq x \leq 9.5[tex]$
B. $[/tex]x \geq 0[tex]$
C. $[/tex]x \leq 50[tex]$
D. $[/tex]x \geq 2$



Answer :

GinnyAnswer
To determine the domain of the given relation for shipping charges, we need to understand the nature of the variable in question, which is the weight of the package in ounces.

In this context, the domain of the relation refers to all possible values of [tex]\( x \)[/tex] (the weight of the package in ounces) that the function can handle.

1. Analyzing the variable [tex]\( x \)[/tex]:
- [tex]\( x \)[/tex] represents the weight of the package in ounces.
- The weight of a package cannot be negative as negative weight does not make physical sense. Therefore, the minimum value for [tex]\( x \)[/tex] must be 0.

2. Upper Bound of [tex]\( x \)[/tex]:
- The problem does not specify any maximum weight limit for packages that can be shipped. This implies that there is no upper bound for [tex]\( x \)[/tex].

From these points, we conclude that the weight [tex]\( x \)[/tex] can be any non-negative value. This means that [tex]\( x \)[/tex] can be any value starting from 0 and can extend indefinitely without any upper limit.

Thus, the correct answer choice that fits this description is:

B. [tex]\( x \geq 0 \)[/tex]

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