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3.1.4: Function Notation and Evaluating Functions

A farmer wants to convert 3 greenhouses to solar power. The smallest greenhouse needs 1,500 square feet of solar panels; the middle and largest greenhouses need 2,100 and 2,800 square feet of panels, respectively. The farmer gets bids from 3 different companies, each with different pricing. The prices are as follows on the next slide:

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3.1.4: Function Notation and Evaluating Functions

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3.1.4: Function Notation and Evaluating Functions

• Company A charges $2,000 for installation per building and $2.00 per square foot of panels. The function for this situation is yA = 2000 + 2(x).

• Company B charges $3,000 for installation per building and $1.50 per square foot of panels. The function for this situation is yB = 3000 + 1.5(x).

• Company C charges $4,200 for installation per building and $1.00 per square foot of panels. The function for this situation is yC = 4200 + x.

1. Which company will charge the least for the smallest greenhouse?

2. Which company will charge the least for the middle greenhouse?

3. Which company will charge the least for the largest greenhouse?

4. If the farmer goes with one company for all three greenhouses, which company will be the least expensive?

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3.1.4: Function Notation and Evaluating Functions

1. Which company will charge the least for the smallest greenhouse?• The smallest greenhouse requires 1,500 square

feet of solar panels, so evaluate A, B, and C at 1,500:

yA = 2000 + 2(1500) = 2000 + 3000 = 5000

yB = 3000 + 1.5(1500) = 3000 + 2250 = 5250

yC = 4200 + (1500) = 5700

• Company A’s bid is the lowest, at $5,000, so it has the least expensive plan for the smallest greenhouse.

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3.1.4: Function Notation and Evaluating Functions

2. Which company will charge the least for the middle greenhouse?• The middle greenhouse requires 2,100 square feet

of solar panels, so evaluate A, B, and C at 2,100:

yA = 2000 + 2(2100) = 2000 + 4200 = 6200

yB = 3000 + 1.5(2100) = 3000 + 3150 = 6150

yC = 4200 + (2100) = 6300

• Company B’s bid is the lowest, at $6,150, so it has the least expensive plan for the middle greenhouse.

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3.1.4: Function Notation and Evaluating Functions

3. Which company will charge the least for the largest greenhouse?• The largest greenhouse requires 2,800 square feet

of solar panels, so evaluate A, B, and C at 2,800:

yA = 2000 + 2(2800) = 2000 + 5600 = 7600

yB = 3000 + 1.5(2800) = 3000 + 4200 = 7200

yC = 4200 + (2800) = 7000

• Company C’s bid is the lowest, at $7,000, so it has the least expensive plan for the largest greenhouse.

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3.1.4: Function Notation and Evaluating Functions

4. If the farmer goes with one company for all three greenhouses, which company will be the least expensive?

yA = 5000 + 6200 + 7600 = 18,800

yB = 5250 + 6150 + 7200 = 18,600

yC = 5700 + 6300 + 7000 = 19,000

• Company B’s total bid is lowest, at $18,600, so it has the least expensive plan to complete the project for all three greenhouses.

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3.1.4: Function Notation and Evaluating Functions