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Suppose you set up a function to show how many hot dogs you will purchase for a dinner when you have already bought two packages but must buy more: [tex]f(h) = 8h + 16[/tex]. What is the domain of this function?

A. [tex]h \ \textgreater \ 0[/tex], only integers
B. [tex]h \ \textgreater \ 0[/tex], all positive numbers
C. all real numbers
D. [tex]h \leq 0[/tex], only integers



Answer :

GinnyAnswer
To determine the domain of the function [tex]\( f(h) = 8h + 16 \)[/tex], let's carefully understand what the function represents and any constraints on [tex]\(h\)[/tex].

1. Understanding the function: The function [tex]\( f(h) = 8h + 16 \)[/tex] calculates the number of hot dogs you will purchase for a dinner. Here, [tex]\( h \)[/tex] represents the number of additional packages of hot dogs you plan to buy.

2. Initial conditions: You have already bought two packages of hot dogs. The term "additional packages" means you are considering only the number of packages beyond those initial two.

3. Analyzing the domain:
- Since you already have two packages, and you're looking to buy more, [tex]\( h \)[/tex] must be positive.
- There is no restriction given that [tex]\( h \)[/tex] has to be an integer. Therefore, [tex]\( h \)[/tex] can be any positive number, whether an integer or not.

Given this understanding, the domain must include all positive numbers greater than zero.

Thus, the domain of the function [tex]\( f(h) = 8h + 16 \)[/tex] is:
[tex]\[ h > 0, \text{ all positive numbers.} \][/tex]

So, the correct option is: [tex]\( h > 0 \)[/tex], all positive numbers.

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