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Warm Up Wed 8/31/16 Read the problem about the farmer, help him decide which company to go with by answering the questions! You may discuss with your partner.

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Presentation on theme: "Warm Up Wed 8/31/16 Read the problem about the farmer, help him decide which company to go with by answering the questions! You may discuss with your partner."— Presentation transcript:

1 Warm Up Wed 8/31/16 Read the problem about the farmer, help him decide which company to go with by answering the questions! You may discuss with your partner. Sit in your same seat as yesterday! Turn in letters signed, info sheets, and schoolnet homework in the homework bin! 1 2.1.4: Function Notation and Evaluating Functions

2 Check it out! 2 2.1.4: Function Notation and Evaluating Functions

3 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: 3 2.1.4: 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 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.

4 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 2.1.4: Function Notation and Evaluating Functions

5 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 2.1.4: Function Notation and Evaluating Functions

6 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 2.1.4: Function Notation and Evaluating Functions

7 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 2.1.4: Function Notation and Evaluating Functions

8 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 2.1.4: Function Notation and Evaluating Functions

9 Schoolnet 1.1 2.1.4: Function Notation and Evaluating Functions 9 Which of the following is the range of the function given the domain?

10 Schoolnet 1.1 2.1.4: Function Notation and Evaluating Functions 10 What is the domain of the function

11 Schoolnet 1.1 # A all integers B all real numbers Call whole numbers D all rational numbers 2.1.4: Function Notation and Evaluating Functions 11 A company uses the function f(x) = 20x – 500 to calculate profit or loss, where x is the number of products sold. What is the most appropriate domain of the function?

12 Schoolnet 1.1 A all integers B all real numbers Call whole numbers D all rational numbers 2.1.4: Function Notation and Evaluating Functions 12 A company uses the function f(x) = 20x – 500 to calculate profit or loss, where x is the number of products sold. What is the most appropriate domain of the function?

13 Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its domain. But, can a function be applied to expressions other than x? What would it mean if we wrote f(2x) or f(x + 1)? In this lesson, we will explore function notation and the versatility of functions. 13 2.1.4: Function Notation and Evaluating Functions

14 Evaluating Functions For example, let f be a function with the domain {1, 2, 3} and let f(x) = 2x. To evaluate f over the domain {1, 2, 3}, we would write the following equations by substituting each value in the domain for x: f(1) = 2(1) = 2 f(2) = 2(2) = 4 f(3) = 2(3) = 6 {2, 4, 6} is the range of f(x). 14 2.1.4: Function Notation and Evaluating Functions

15 Key Concepts Functions can be evaluated at values and variables. To evaluate a function, substitute the values for the domain for all occurrences of x. To evaluate f(2) in f(x) = x + 1, replace all x’s with 2 and simplify: f(2) = (2) + 1 = 3. This means that f(2) = 3. (x, (f(x)) is an ordered pair of a function and a point on the graph of the function. 15 2.1.4: Function Notation and Evaluating Functions

16 Common Errors/Misconceptions thinking function notation means “f times x” instead of “f of x” trying to multiply the left side of the function notation 16 2.1.4: Function Notation and Evaluating Functions

17 Guided Practice Example 1 Evaluate f(x) = 4x – 7 over the domain {1, 2, 3, 4}. What is the range? 17 2.1.4: Function Notation and Evaluating Functions

18 Guided Practice: Example 1, continued 1.To evaluate f(x) = 4x – 7 over the domain {1, 2, 3, 4}, substitute the values from the domain into f(x) = 4x – 7. 18 2.1.4: Function Notation and Evaluating Functions

19 Guided Practice: Example 1, continued 2.Evaluate f(1). 19 2.1.4: Function Notation and Evaluating Functions f(x) = 4x – 7Original function f(1) = 4(1) – 7Substitute 1 for x. f(1) = 4 – 7 = –3Simplify.

20 Guided Practice: Example 1, continued 3.Evaluate f(2). 20 2.1.4: Function Notation and Evaluating Functions f(x) = 4x – 7Original function f(2) = 4(2) – 7Substitute 2 for x. f(2) = 8 – 7 = 1Simplify.

21 Guided Practice: Example 1, continued 4.Evaluate f(3). 21 2.1.4: Function Notation and Evaluating Functions f(x) = 4x – 7Original function f(3) = 4(3) – 7Substitute 3 for x. f(3) = 12 – 7 = 5Simplify.

22 Guided Practice: Example 1, continued 5.Evaluate f(4). 22 2.1.4: Function Notation and Evaluating Functions f(x) = 4x – 7Original function f(4) = 4(4) – 7Substitute 4 for x. f(4) = 16 – 7 = 9Simplify.

23 Guided Practice: Example 1, continued 6.Collect the set of outputs from the inputs. The range is {–3, 1, 5, 9}. 23 2.1.4: Function Notation and Evaluating Functions ✔

24 24 2.1.4: Function Notation and Evaluating Functions Guided Practice: Example 1, continued 24

25 25 2.1.4: Function Notation and Evaluating Functions

26 Guided Practice Example 3 Raven started an online petition calling for more vegan options in the school cafeteria. So far, the number of signatures has doubled every day. She started with 32 signatures on the first day. Raven’s petition can be modeled by the function f(x) = 32(2) x. Evaluate f(3) and interpret the results in terms of the petition. 26 2.1.4: Function Notation and Evaluating Functions

27 Guided Practice: Example 3, continued 1.Evaluate the function. 27 2.1.4: Function Notation and Evaluating Functions f(x) = 32(2) x Original function f(3) = 32(2) 3 Substitute 3 for x. f(3) = 32(8)Simplify as needed. f(3) = 256

28 Guided Practice: Example 3, continued 2.Interpret the results. On day 3, the petition has 256 signatures. This is a point on the graph, (3, 256), of the function f(x) = 32(2) x. 28 2.1.4: Function Notation and Evaluating Functions

29 Guided Practice: Example 3, continued 29 2.1.4: Function Notation and Evaluating Functions ✔ Number of signatures Days

30 30 2.1.4: Function Notation and Evaluating Functions Guided Practice: Example 3, continued 30

31 31 2.1.4: Function Notation and Evaluating Functions

32 32 2.1.4: Function Notation and Evaluating Functions

33 33 2.1.4: Function Notation and Evaluating Functions

34 PRACTICE #1-10 With your partner, practice evaluating functions over the specified domain. For questions #7-10, remember to: Then complete the Problem Based Task : Party Time with your partner! Turn in one paper! 34 2.1.4: Function Notation and Evaluating Functions

35 If you finish the practice early or would like extra practice, raise your hand and Mrs. Sawyer will bring you more problems to master! 35 2.1.4: Function Notation and Evaluating Functions

36 Homework Schoolnet 1.2 Code: SAWYER12 Bring back Student Info Sheet & Course Letter Signed! Bring in tissues, hand sanitizer, paper towels, or Lysol spray to donate! 36 2.1.4: Function Notation and Evaluating Functions

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