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A caterer has 5 rolls. He is ordering more rolls. He can order up to 9 packages of rolls, and each package contains 12 rolls. The caterer cannot order partial packages. The function that models the number of rolls the caterer has is [tex]f(p) = 12p + 5[/tex], where [tex]p[/tex] is the number of packages he orders.

What is the practical domain of the function?

A. all real numbers
B. all real numbers from 1 to 9, inclusive
C. all integers from 1 to 9, inclusive
D. [tex]\{17, 29, 41, 53, 65, 77, 89, 101, 113\}[/tex]

Sagot :

GinnyAnswer
To determine the practical domain of the function [tex]\( f(p) = 12p + 5 \)[/tex], we need to consider what values of [tex]\( p \)[/tex] are realistic in the context of the problem.

Here, [tex]\( p \)[/tex] represents the number of packages of rolls the caterer can order. Since each package contains 12 rolls, the number of packages [tex]\( p \)[/tex] must be a whole number (integer), and it cannot be zero or a negative number because the number of packages ordered must make sense in the context of ordering rolls.

Additionally, the caterer can order up to 9 packages of rolls. Therefore, [tex]\( p \)[/tex] must be a whole number between 1 and 9, inclusive.

The practical domain, in this case, is the set of all integer values between 1 and 9, inclusive. Thus, [tex]\( p \)[/tex] can be any integer from 1 to 9.

The practical domain of the function [tex]\( f(p) = 12p + 5 \)[/tex] is therefore:
[tex]\[ \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \][/tex]

This corresponds to the set of all integers from 1 to 9, inclusive, making the proper choice the option: "all integers from 1 to 9, inclusive".
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