Question

A function, fx), represents the height of a plant x months after being planted. Students measure and record the height on a monthly basis.

Select the appropriate domain for this situation.
OA
the set of all integers
OB. the set of all positive real numbers
OC. the set of all positive integers.
OD. the set of all real numbers

Answer 1

C. the set of all positive integers

Explanation:

You want to know the appropriate domain of the function f(x) where x is months after a plant was planted, and f(x) is the height of the plant.

Domain

The domain of a function is the set of values of the independent variable for which the function is defined. In this case, the independent variable is x, the number of months after the plant was planted. Months are counted using the natural numbers, the set of all positive integers.

The appropriate domain is the set of all positive integers.

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Additional comment

As a practical matter, the domain will have an upper limit, so will not actually be all positive integers.

The range of function values is likely the set of positive real numbers, though it might be integers if the measurements are recorded as integer values (mm or cm or in, for example).