Janelle is planning to knit scarves to give to her friends and family members on Valentine's day. She will need to purchase $200$ yards of yarn for each scarf that she is going to knit. The function $Y(s)$ represents the amount of yarn Janelle will need, in yards, in order to knit $s$ scarves. $\newline$ What is the domain of $Y(s)$ ? $\newline$ Choices: $\newline$ (A) all multiples of $200$ from $0$ to $2,000$ $\newline$ (B) all whole numbers from $0$ to $200$ $\newline$ (C) all multiples of $200$ greater than or equal to $0$ $\newline$ (D) all whole numbers

Full solution

Q. Janelle is planning to knit scarves to give to her friends and family members on Valentine's day. She will need to purchase

200

yards of yarn for each scarf that she is going to knit. The function

Y(s)

represents the amount of yarn Janelle will need, in yards, in order to knit

s

scarves.

\newline

What is the domain of

Y(s)

\newline

Choices:

\newline

(A) all multiples of

200

from

0

2,000

\newline

(B) all whole numbers from

0

200

\newline

200

greater than or equal to

0

\newline

(D) all whole numbers

Understand Y(s) Function: Understand the function $Y(s)$ and what it represents. $\newline$ The function $Y(s) = 200s$ represents the amount of yarn, in yards, that Janelle will need to knit $s$ scarves. Since each scarf requires $200$ yards of yarn, the total yarn needed is directly proportional to the number of scarves she plans to knit.
Determine Possible Values: Determine the possible values for $s$ . Since $s$ represents the number of scarves, it must be a whole number. Janelle cannot knit a fraction of a scarf, so $s$ cannot be a fraction or a negative number. Therefore, $s$ must be a whole number that is greater than or equal to $0$ .
Identify Domain Context: Identify the domain based on the context of the problem. $\newline$ The domain of a function is the set of all possible input values. In this case, the input value is the number of scarves, $s$ . Since $s$ must be a whole number and there is no upper limit given in the problem for the number of scarves Janelle can knit, the domain is all whole numbers greater than or equal to $0$ .
Match Domain with Choices: Match the correct domain with the given choices. $\newline$ The domain we determined is all whole numbers greater than or equal to $0$ . This matches with choice (D) all whole numbers.