HW Writing functions Rules d2.pdf - Free Printable

Let's solve each problem step by step.

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Problem 1: Bananas cost $0.40 per pound

#### Step 1: Fill in the table

We are given:
- Cost per pound = $0.40
- So, total cost = number of pounds × $0.40

| Number of pounds | 1 | 2 | 3 | 4 | 5 | x |
|------------------|-------|-------|-------|-------|-------|-------|
| Total cost | 0.40 | 0.80 | 1.20 | 1.60 | 2.00 | 0.40x |

Calculations:
- 1 × 0.40 = 0.40
- 2 × 0.40 = 0.80
- 3 × 0.40 = 1.20
- 4 × 0.40 = 1.60
- 5 × 0.40 = 2.00
- x × 0.40 = 0.40x

#### Step 2: Identify independent and dependent variables

- Independent (x): Number of pounds (this is what we choose)
- Dependent f(x): Total cost (depends on how many pounds you buy)

#### Step 3: Write a function rule

Since cost = 0.40 × number of pounds:

> Function Rule: f(x) = 0.40x

#### Step 4: Use the function to find cost for 3.5 pounds

f(3.5) = 0.40 × 3.5 = $1.40

✔ Answer: It would cost $1.40 to buy 3.5 pounds of bananas.

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Problem 2: Renting a cabin costs $50 plus $10 per person

#### Step 1: Fill in the table

Fixed cost = $50
Per person cost = $10
So total cost = 50 + 10 × number of people

| Number of people | 1 | 2 | 3 | 4 | 5 | x |
|------------------|-------|-------|-------|-------|-------|-------|
| Total cost | 60 | 70 | 80 | 90 | 100 | 50 + 10x |

Calculations:
- 1: 50 + 10×1 = 60
- 2: 50 + 10×2 = 70
- 3: 50 + 10×3 = 80
- 4: 50 + 10×4 = 90
- 5: 50 + 10×5 = 100
- x: 50 + 10x

#### Step 2: Identify variables

- Independent (x): Number of people
- Dependent f(x): Total cost

#### Step 3: Function rule

> Function Rule: f(x) = 50 + 10x

#### Step 4: Find total cost for 7 people

f(7) = 50 + 10×7 = 50 + 70 = $120

✔ Answer: The total cost for seven people is $120.

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Problem 3: Pens are shipped in boxes of 12

This one is incomplete — no question is asked yet. But based on context, likely we need to write a function rule for the number of pens based on number of boxes.

Let’s assume:
- Each box has 12 pens
- Let x = number of boxes
- Then total pens = 12x

#### Table (if needed):

| Number of boxes | 1 | 2 | 3 | 4 | 5 | x |
|------------------|---|---|---|---|---|---|
| Total pens | 12| 24| 36| 48| 60| 12x |

- Independent (x): Number of boxes
- Dependent f(x): Total number of pens
- Function Rule: f(x) = 12x

If there were a specific question (e.g., "How many pens in 8 boxes?"), we'd plug in x = 8 → f(8) = 96.

But since no specific question is stated, we can only provide the function rule.

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✔ Final Answers Summary:

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1.) Bananas

- Table filled as above.
- Independent (x): Number of pounds
- Dependent f(x): Total cost
- Function Rule: f(x) = 0.40x
- Cost for 3.5 pounds: $1.40

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2.) Cabin Rental

- Table filled as above.
- Independent (x): Number of people
- Dependent f(x): Total cost
- Function Rule: f(x) = 50 + 10x
- Cost for 7 people: $120

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3.) Pens

- Independent (x): Number of boxes
- Dependent f(x): Total number of pens
- Function Rule: f(x) = 12x

(No specific question asked, but this is the standard function for this situation.)

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