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Check it out! 1 3.1.4: Function Notation and Evaluating Functions

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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: 2 3.1.4: Function Notation and Evaluating Functions

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3 Company A charges $2,000 for installation per building and $2.00 per square foot of panels. The function for this situation is y A = 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 y B = 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 y C = 4200 + x.

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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? 4 3.1.4: Function Notation and Evaluating Functions

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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: y A = 2000 + 2(1500) = 2000 + 3000 = 5000 y B = 3000 + 1.5(1500) = 3000 + 2250 = 5250 y C = 4200 + (1500) = 5700 Company A’s bid is the lowest, at $5,000, so it has the least expensive plan for the smallest greenhouse. 5 3.1.4: Function Notation and Evaluating Functions

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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: y A = 2000 + 2(2100) = 2000 + 4200 = 6200 y B = 3000 + 1.5(2100) = 3000 + 3150 = 6150 y C = 4200 + (2100) = 6300 Company B’s bid is the lowest, at $6,150, so it has the least expensive plan for the middle greenhouse. 6 3.1.4: Function Notation and Evaluating Functions

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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: y A = 2000 + 2(2800) = 2000 + 5600 = 7600 y B = 3000 + 1.5(2800) = 3000 + 4200 = 7200 y C = 4200 + (2800) = 7000 Company C’s bid is the lowest, at $7,000, so it has the least expensive plan for the largest greenhouse. 7 3.1.4: Function Notation and Evaluating Functions

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4.If the farmer goes with one company for all three greenhouses, which company will be the least expensive? y A = 5000 + 6200 + 7600 = 18,800 y B = 5250 + 6150 + 7200 = 18,600 y C = 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. 8 3.1.4: Function Notation and Evaluating Functions

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