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## 3-3

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**3-3**Writing Functions Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1**Objectives**Identify independent and dependent variables. Write an equation in function notation Evaluate a function for given input values.**Vocabulary**independent variable dependent variable function rule function notation**Input /Independent**Domain x function f(x) y Range Output /Dependent**Identify the independent and dependent variables.**• A painter must measure a room before deciding how much paint to buy. The amount of paintdepends on the size of a room. Dependent: amount of paint Independent: measurement of the room 2) The height of a candle decreases d centimeters for every hour it burns. The height of a candledependson the # of hours it burns. Dependent: height of candle Independent: # of hours**3) A company charges $10 per hour to rent a jackhammer.**The cost to rent a jackhammerdependson the length of time it is rented. Dependent variable: cost Independent variable: time 4) Apples cost $0.99 per pound. The cost of applesdepends on the number of pounds bought. Dependent variable: cost Independent variable: pounds**10 – 4 2**5 – 4 = 1 or Determine a relationship between the x- and y-values. 5 10 15 20 1 3 2 4 Step 1 List possible relationships between the first x and y Step 2 Write an equation. or f(x) = (1/5)x function notation Read as: f of x / function of x**{(1, 3), (2, 6), (3, 9), (4, 12)}**x 4 1 2 3 y 3 6 9 12 Step 1 List possible relationships between the first x and y 1 3 = 3 or 1 + 2 = 3 2 • 3 = 6 2 + 2 6 Step 2 Write an equation. y = 3x or f(x) = 3x function notation Read as: f of x / function of x**Identify the independent and dependent variables. Write an**equation in function notation for the situation. A math tutor charges $35 per hour. Dependent: fee Independent: hours Let h represent the number of hours of tutoring. The function isf(h) = 35h A fitness center charges a $100 initiation fee plus $40 per month. Dependent: total cost Independent: number of months Let mrepresent the number of months The function is f(m) = 40m + 100.**You can think of a function as an input-output machine. For**Tasha’s earnings, f(x) = 5x. If you input a value x, the output is 5x. input x 2 6 function f(x)=5x 5x 10 30 output**WARM UP**Look at the pattern 1) Draw the 5th and the 6th figures. 2) Use the table to fill in the information • 3) Write an equation to show the relationship between x and y • 4) How many squares will be used in the 20th figure?**Identify the independent and dependent variables. Write an**equation in function notation for the situation. 1) A math tutor charges $35 per hour. y Dependent: fee Independent: hours x The function isy = 35x ORf(x) = 35x 2) A fitness center charges a $100 initiation fee plus $40 per month. y Dependent: total cost Independent: number of months x The function is y = 40x + 100 OR f(x) = 40x + 100**Adnoc needed National day presents for their office staff.**The cost was 150 DHS per staff member present. They also had to pay 750 DHSto have it all shipped from abroad. • a) Identify the dependent and Independent Variables. • b) Write an equation in function for this situation • c) If they bought 250 presents, how much did it cost? • d) If they had 3250 DHS to spend, how may presents could they buy?**Evaluating Functions**You can think of a function as an input-output machine. For Tasha’s earnings, f(x) = 5x. If you input a value x, the output is 5x. input x 2 6 function f(x)=5x 5x 10 30 output**Evaluate the function for the given input values.**f(7) f(-4) f(x) = 3x + 2, find f(x) when x = 7 and when x = –4 f(x) = 3(x) + 2 f(x) = 3(x) + 2 = 3(–4) + 2 = 3(7) + 2 = –12 + 2 = 21 + 2 = 23 = –10**Evaluate the following expressions given the functions**below: g(x) = -3x + 1 f(x) = x2 + 7 h(x) = 12/x j(x) = 2x + 9 • a) g(10) • b) f(3) • c) h(-2) • d) j(7) • e) h(-4)**The flu has spread throughout a town. The function below**determines how many people have the flue, where t=time in days and f(t)=the number of people in thousands. f(t) = 3t – 5 • a) find f(6) • b) what does f(2) mean? c) Find t when f(t) = 16**Lesson Quiz: Part I**Identify the independent and dependent variables. Write an equation in function notation for each situation. 1. A buffet charges $8.95 per person. independent: number of people dependent: cost f(p) = 8.95p 2. A moving company charges $130 for weekly truck rental plus $1.50 per mile. independent: miles dependent: cost f(m) = 130 + 1.50m**Lesson Quiz: Part II**Evaluate each function for the given input values. 3. For g(t) = , find g(t) when t = 20 and when t = –12. g(20) = 2 g(–12) = –6 4. For f(x) = 6x – 1, find f(x) when x = 3.5 and when x = –5. f(3.5) = 20 f(–5) = –31**Lesson Quiz: Part III**Write a function to describe the situation. Find the reasonable domain and range for the function. 5. A theater can be rented for exactly 2, 3, or 4 hours. The cost is a $100 deposit plus $200 per hour. f(h) = 200h + 100 Domain: {2, 3, 4} Range: {$500, $700, $900}