2.1.4: Function Notation and Evaluating Functions Do Now If 9(x − 9) = −11, then x = ? 2.1.4: Function Notation and Evaluating Functions

GOOD THINGS!! 2.1.3: Domain and Range

2.1.4: Function Notation and Evaluating Functions

2.1.4: Function Notation and Evaluating Functions Policy Review Cell phones Sleeping Materials 2.1.4: Function Notation and Evaluating Functions

2.1.4: Function Notation and Evaluating Functions Warm Up Page 25 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. 2.1.4: Function Notation and Evaluating Functions

2.1.4: Function Notation and Evaluating Functions Warm Up Company A charges $2,000 for installation per building and $2.00 per square foot of panels. The function for this situation is f(x)= 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 f(x)= 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 f(x)= 4200 + x. 2.1.4: Function Notation and Evaluating Functions

2.1.4: Function Notation and Evaluating Functions Warm Up: Info Review Greenhouses Small Medium Large 1500 sq. ft. 2100 sq. ft. 2800 sq. ft. Pricing Functions Company A Company B Company C f(x)= 2000 + 2(x) f(x)= 3000 + 1.5(x) f(x)= 4200 + x 8 minutes independent 8 minutes partner 2.1.4: Function Notation and Evaluating Functions

Company A: f(x) = 2000 + 2(1500) = 2000 + 3000 = 5000 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. Company A: f(x) = 2000 + 2(1500) = 2000 + 3000 = 5000 Company B: f(x) = 3000 + 1.5(1500) = 3000 + 2250 =5250 Company C: f(x) = 4200 + (1500) = 5700 Company A’s bid is the lowest, at $5,000, so it has the least expensive plan for the smallest greenhouse. 2.1.4: Function Notation and Evaluating Functions

Company A: f(x)= 2000 + 2(2100) = 2000 + 4200=6200 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: Company A: f(x)= 2000 + 2(2100) = 2000 + 4200=6200 Company B: f(x)= 3000 + 1.5(2100) =3000 + 3150 =6150 Company C: f(x)= 4200 + (2100) = 6300 Company B’s bid is the lowest, at $6,150, so it has the least expensive plan for the middle greenhouse. 2.1.4: Function Notation and Evaluating Functions

Company A: f(x) = 2000 + 2(2800) = 2000 + 5600 = 7600 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: Company A: f(x) = 2000 + 2(2800) = 2000 + 5600 = 7600 Company B: f(x) = 3000 + 1.5(2800) = 3000 + 4200= 7200 Company C: f(x) = 4200 + (2800) = 7000 Company C’s bid is the lowest, at $7,000, so it has the least expensive plan for the largest greenhouse. 2.1.4: Function Notation and Evaluating Functions

If the farmer goes with one company for all three greenhouses, which company will be the least expensive? Company A = 5000 + 6200 + 7600 = 18,800 Company B = 5250 + 6150 + 7200 = 18,600 Company 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. Connection to the Lesson Students will be evaluating functions, which requires substitution, as seen in the warm-up. Students will learn how to evaluate functions like the ones in the warm-up using function notation, which is an easier method to keep track of multiple functions with varying inputs. 2.1.4: Function Notation and Evaluating Functions

2.1.4: Function Notation and Evaluating Functions BRAIN BREAK!!!! What is the value of the square? 2.1.4: Function Notation and Evaluating Functions

Note Taking MUST include: Today’s date (9/6) before you begin notes Essential Question at top of page If you see a that’s my hint to you to put that in your notes Essential Question How is function notation and evaluating functions related to the coordinate plane? 2.1.3: Domain and Range

Introduction Functions f of a variable x are represented by f(x) The range of f(x) is dependent on its domain What is range? What is domain? 2.1.4: Function Notation and Evaluating Functions

Introduction, continued Example: Let f be a function with the domain {1, 2, 3} and let f(x) = 2x To evaluate this function over the domain {1, 2, 3}, we would substitute each value in the domain for x: f(1) = 2(1) = 2 f(2) = 2(2) = 4 f(3) = 2(3) = 6 By solving for the function, we find that {2, 4, 6} is the range of f(x). 2.1.4: Function Notation and Evaluating Functions

Introduction, continued Example: Let f be a function with the domain {1, 2, 3} and let f(x) = 3x + 1 f(1) = 3(1) + 1 = 4 f(2) = 3(2) + 1 =7 f(3) = 3(3) + 1 = 10 The range of f(x) is {4, 7, 10} 2.1.4: Function Notation and Evaluating Functions

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. “x” is the domain, f(x) is the range 2.1.4: Function Notation and Evaluating Functions

Common Errors/Misconceptions Function Notation is NOT a multiplication equation f(x) does NOT mean “f times x” 2.1.4: Function Notation and Evaluating Functions

Work with your elbow partner. Write down answers to check as a class. Partner Practice Work with your elbow partner. Write down answers to check as a class. Evaluate f(x) = 4x – 7 over the domain {1, 2, 3, 4}. What is the range? 2.1.4: Function Notation and Evaluating Functions

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

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

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

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

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

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

Independent Practice Evaluate g(x) = 3x + 1 over the domain {0, 1, 2, 3}. What is the range? Graph the function. 2.1.4: Function Notation and Evaluating Functions

Independent Practice, pt. 2 g(x) = 3x + 1 Range: {2, 4, 10, 28} Graph: Is the point (0, 5) on this graph??? 2.1.4: Function Notation and Evaluating Functions

Guided Practice Raven started a petition calling for more vegetarian 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. 2.1.4: Function Notation and Evaluating Functions

f(x) = 32(2)x f(3) = 32(2)3 f(3) = 32(8) f(3) = 256 Guided Practice: Raven’s petition Evaluate the function. f(x) = 32(2)x f(3) = 32(2)3 f(3) = 32(8) f(3) = 256 2.1.4: Function Notation and Evaluating Functions

X y range domain input output Guided Practice: Raven’s petition Interpret the results. On day 3, the petition has 256 signatures. This is a point (3, 256) on the graph of the function f(x)=32(2)x **3 is the INPUT, 256 is the OUTPUT X y range domain input output 2.1.4: Function Notation and Evaluating Functions

Guided Practice: Raven’s petition Number of signatures Days ✔ Input = x Output = y 2.1.4: Function Notation and Evaluating Functions

2.1.4: Function Notation and Evaluating Functions PARTY TIME (pg. 29) A company is throwing a large party requiring a venue, tables, chairs, and waiters. There will be between 50 and 200 guests, so the party coordinator has been asked to predict the total cost of the event for 50, 100, 150, and 200 guests. The functions below describe the number of tables, chairs, and waiters needed, as well as the size of the venue in square feet. In each equation, x represents the number of guests. 2.1.4: Function Notation and Evaluating Functions

2.1.4: Function Notation and Evaluating Functions PARTY TIME pt. 2 Tables are $50 each, chairs are $3 each, waiters earn $100 each, and venues charge $2 per square foot. Total cost estimate: 2.1.4: Function Notation and Evaluating Functions

2.1.4: Function Notation and Evaluating Functions PARTY TIME Questions a. What is the domain of t(x)? b. What is the domain of c(x)? c. What is the domain of w(x)? d. What is the domain of s(x)? e. What is the domain of P(x)? f. What is the most the venue can cost? g. What is the cost for tables and chairs for 100 guests? h. What is the entire cost of the party for 150 guests? i. What is the least amount the party can cost? j. Complete a table of values for the costs of the party. 2.1.4: Function Notation and Evaluating Functions

2.1.4: Function Notation and Evaluating Functions PARTY TIME Table # Guests Tables t(x) Chairs c(x) Waiters w(x) Venue v(x) Total Cost 50 100 150 200 2.1.4: Function Notation and Evaluating Functions

2.1.4: Function Notation and Evaluating Functions Exit Ticket Pull out 1 sheet of paper Due by end of class 1. Evaluate f(x) = 2x +4 over the domain {0, 1, 2, 3}. What is the range of f(x)? 2. Is the point (1,7) a point on the graph of this function? Why or why not? 2.1.4: Function Notation and Evaluating Functions