Domain and Range - Time Flies Edu - Free Printable

Let's solve each situation step by step.

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1. Cynthia is selling candy for her class fundraiser. She has a box of 20 candy bars that are $2 each.

#### Step 1: Identify the variables
- Independent variable: This is the variable that you can control or choose. In this case, Cynthia chooses how many candy bars she sells.
- So, the number of candy bars sold is the independent variable.

- Dependent variable: This depends on the independent variable. The total money earned depends on how many candy bars are sold.
- So, the total money earned is the dependent variable.

#### Step 2: Reasonable Domain
- Domain refers to the possible values the independent variable (number of candy bars sold) can take.
- She has 20 candy bars, so she can sell anywhere from 0 to 20 candy bars.
- So, the reasonable domain is:
{0, 1, 2, ..., 20} or in interval notation: [0, 20] (whole numbers only).

#### Step 3: Reasonable Range
- Range refers to the possible values of the dependent variable (money earned).
- Each candy bar is $2, so:
- If she sells 0 bars → $0
- If she sells 20 bars → 20 × $2 = $40
- So, the reasonable range is:
{0, 2, 4, ..., 40} or in interval notation: [0, 40] (even numbers only, since each sale adds $2).

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✔ Answer for Problem 1:

- Independent variable: Number of candy bars sold
- Dependent variable: Total money earned
- Reasonable Domain: 0 to 20 (whole numbers)
- Reasonable Range: $0 to $40 (in increments of $2)

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2. Carlos is a barber. He sees at most 18 customers in a day. He charges $15 for each haircut.

#### Step 1: Identify the variables
- Independent variable: Number of customers (he can choose how many he serves, up to 18)
- Dependent variable: Total earnings (depends on number of customers)

#### Step 2: Reasonable Domain
- He sees at most 18 customers, and at least 0.
- So, number of customers can be:
{0, 1, 2, ..., 18}
→ Domain: [0, 18] (whole numbers)

#### Step 3: Reasonable Range
- Each customer pays $15.
- So, if 0 customers → $0
If 18 customers → 18 × $15 = $270
- So, earnings go from $0 to $270 in $15 increments.
- Range: {0, 15, 30, ..., 270} → [0, 270] in $15 steps

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✔ Answer for Problem 2:

- Independent variable: Number of customers served
- Dependent variable: Total amount of money earned
- Reasonable Domain: 0 to 18 (whole numbers)
- Reasonable Range: $0 to $270 (in increments of $15)

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Final Answers:

| Problem | Independent Variable | Dependent Variable | Reasonable Domain | Reasonable Range |
|--------|-----------------------|--------------------|-------------------|------------------|
| 1 | Number of candy bars sold | Total money earned | 0 to 20 (whole numbers) | $0 to $40 (in $2 increments) |
| 2 | Number of customers served | Total money earned | 0 to 18 (whole numbers) | $0 to $270 (in $15 increments) |

Let me know if you'd like this written out in a table format or formatted for submission!