The appropriate functions whose domains are all positive integers are those where the input variable represents a count or quantity that cannot be negative or fractional.
Out of the options provided:
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A: The function f(n) models the size of a jar that holds n marbles. (This is valid for positive integers since you cannot have a jar holding a negative number of marbles.)
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B: The function f(y) models the number of inches a tree grows in n years. (This may imply time in years, which is generally a positive integer, but the growth can be represented in real numbers, not just integers.)
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C: The function f(r) models the circumference of a balloon based on radius, r. (The radius can be a positive real number, not just an integer.)
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D: The function f(s) models the population of mice based on the number of n snakes in an ecosystem. (The number of snakes is discrete but we cannot specify that n must be positive integers merely from the relationship.)
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E: The function f(n) models the amount of labor-hours it takes to construct n televisions that are ready to be sold. (This is valid for positive integers since you cannot construct a negative number of televisions.)
Therefore, the functions where the appropriate domain is all positive integers are A and E.
1 answer