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.
