Download presentation

Presentation is loading. Please wait.

Published bySamuel Kennedy Modified over 2 years ago

1
Holt Algebra Writing Functions 4-3 Writing Functions Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

2
Holt Algebra Writing Functions Warm Up Evaluate each expression for a = 2, b = –3, and c = a + 3c 2. ab – c c + b 4. 4c – b 5. b a + c 26 –

3
Holt Algebra Writing Functions Identify independent and dependent variables. Write an equation in function notation and evaluate a function for given input values. Objectives

4
Holt Algebra Writing Functions independent variable dependent variable function rule function notation Vocabulary

5
Holt Algebra Writing Functions Example 1: Using a Table to Write an Equation Determine a relationship between the x- and y-values. Write an equation. x y Step 1 List possible relationships between the first x and y-values. 5 – 4 = 1 and

6
Holt Algebra Writing Functions Example 1 Continued Step 2 Determine which relationship works for the other x- and y- values. 10 – 4 2 and15 – 4 3 and 20 – 4 4 and The value of y is one-fifth,, of x. Step 3 Write an equation. or The value of y is one-fifth of x.

7
Holt Algebra Writing Functions Check It Out! Example 1 Determine a relationship between the x- and y-values. Write an equation. {(1, 3), (2, 6), (3, 9), (4, 12)} x y Step 1 List possible relationships between the first x- and y-values. 1 3 = 3 and = 3

8
Holt Algebra Writing Functions y = 3x Check It Out! Example 1 Continued Step 2 Determine which relationship works for the other x- and y- values. 2 3 = = = The value of y is 3 times x. Step 3 Write an equation. The value of y is 3 times x.

9
Holt Algebra Writing Functions The equation in Example 1 describes a function because for each x-value (input), there is only one y-value (output).

10
Holt Algebra Writing Functions The input of a function is the independent variable. The output of a function is the dependent variable. The value of the dependent variable depends on, or is a function of, the value of the independent variable.

11
Holt Algebra Writing Functions Example 2A: Identifying Independent and Dependent Variables Identify the independent and dependent variables in the situation. A painter must measure a room before deciding how much paint to buy. The amount of paint depends on the measurement of a room. Dependent: amount of paint Independent: measurement of the room

12
Holt Algebra Writing Functions Identify the independent and dependent variables in the situation. The height of a candle decrease d centimeters for every hour it burns. Dependent: height of candle Independent: time The height of a candle depends on the number of hours it burns. Example 2B: Identifying Independent and Dependent Variables

13
Holt Algebra Writing Functions A veterinarian must weight an animal before determining the amount of medication. The amount of medication depends on the weight of an animal. Dependent: amount of medication Independent: weight of animal Identify the independent and dependent variables in the situation. Example 2C: Identifying Independent and Dependent Variables

14
Holt Algebra Writing Functions Helpful Hint There are several different ways to describe the variables of a function. Independent Variable Dependent Variable x-values y-values DomainRange InputOutput xf(x)f(x)

15
Holt Algebra Writing Functions Check It Out! Example 2a A company charges $10 per hour to rent a jackhammer. Identify the independent and dependent variable in the situation. The cost to rent a jackhammer depends on the length of time it is rented. Dependent variable: cost Independent variable: time

16
Holt Algebra Writing Functions Identify the independent and dependent variable in the situation. Check It Out! Example 2b Camryn buys p pounds of apples at $0.99 per pound. The cost of apples depends on the number of pounds bought. Dependent variable: cost Independent variable: pounds

17
Holt Algebra Writing Functions An algebraic expression that defines a function is a function rule. If x is the independent variable and y is the dependent variable, then function notation for y is f(x), read f of x, where f names the function. When an equation in two variables describes a function, you can use function notation to write it.

18
Holt Algebra Writing Functions The dependent variable is a function of the independent variable. y is a function of x. y = f (x)

19
Holt Algebra Writing Functions Identify the independent and dependent variables. Write a rule in function notation for the situation. A math tutor charges $35 per hour. The function for the amount a math tutor charges is f(h) = 35h. Example 3A: Writing Functions The amount a math tutor charges depends on number of hours. Dependent: charges Independent: hours Let h represent the number of hours of tutoring.

20
Holt Algebra Writing Functions A fitness center charges a $100 initiation fee plus $40 per month. The function for the amount the fitness center charges is f(m) = 40m Example 3B: Writing Functions Identify the independent and dependent variables. Write a rule in function notation for the situation. The total cost depends on the number of months, plus $100. Dependent: total cost Independent: number of months Let m represent the number of months

21
Holt Algebra Writing Functions Check It Out! Example 3a Identify the independent and dependent variables. Write a rule in function notation for the situation. Steven buys lettuce that costs $1.69/lb. The function for cost of the lettuce is f(x) = 1.69x. The total cost depends on how many pounds of lettuce that Steven buys. Dependent: total cost Independent: pounds Let x represent the number of pounds Steven bought.

22
Holt Algebra Writing Functions Check It Out! Example 3b Identify the independent and dependent variables. Write a rule in function notation for the situation. An amusement park charges a $6.00 parking fee plus $29.99 per person. The function for the total park cost is f(x) = 29.99x + 6. The total cost depends on the number of persons in the car, plus $6. Dependent: total cost Independent: number of persons in the car Let x represent the number of persons in the car.

23
Holt Algebra Writing Functions You can think of a function as an input-output machine. input 10 x function f(x)=5x output 5x5x

24
Holt Algebra Writing Functions Example 4A: Evaluating Functions Evaluate the function for the given input values. For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4. = f(7) = 3(7) + 2 Substitute 7 for x. f(x) = 3(x) + 2 = 23 Simplify. f(x) = 3(x) + 2 f(–4) = 3(–4) + 2 Substitute –4 for x. Simplify. = – = –10

25
Holt Algebra Writing Functions Example 4B: Evaluating Functions Evaluate the function for the given input values. For g(t) = 1.5t – 5, find g(t) when t = 6 and when t = –2. g(t) = 1.5t – 5 g(6) = 1.5(6) – 5 = 9 – 5 = 4 g(–2) = 1.5(–2) – 5 = –3 – 5 = –8

26
Holt Algebra Writing Functions Example 4C: Evaluating Functions Evaluate the function for the given input values. For, find h(r) when r = 600 and when r = –12. = 202= – 2

27
Holt Algebra Writing Functions Check It Out! Example 4a Evaluate the function for the given input values. For h(c) = 2c – 1, find h(c) when c = 1 and when c = –3. h(c) = 2c – 1 h(1) = 2(1) – 1 = 2 – 1 = 1 h(c) = 2c – 1 h(–3) = 2( – 3) – 1 = –6 – 1 = – 7

28
Holt Algebra Writing Functions Check It Out! Example 4b Evaluate each function for the given input values. For g(t) =, find g(t) when t = –24 and when t = 400. = – 5 = 101

29
Holt Algebra Writing Functions When a function describes a real-world situation, every real number is not always reasonable for the domain and range. For example, a number representing the length of an object cannot be negative, and only whole numbers can represent a number of people.

30
Holt Algebra Writing Functions Example 5: Finding the Reasonable Range and Domain of a Function Write a function to describe the situation. Find a reasonable domain and range of the function. Joe has enough money to buy 1, 2, or 3 DVDs at $15.00 each. Money spentis $15.00 for each DVD. f(x) = $15.00 x If Joe buys x DVDs, he will spend f(x) = 15x dollars. Joe only has enough money to purchase 1, 2, or 3 DVDs. A reasonable domain is {1, 2, 3}.

31
Holt Algebra Writing Functions Example 5 Continued Substitute the domain values into the function rule to find the range values. x f(x)f(x) 15(1) = 15 15(2) = 30 15(3) = 45 A reasonable range for this situation is {$15, $30, $45}.

32
Holt Algebra Writing Functions Check It Out! Example 5 The settings on a space heater are the whole numbers from 0 to 3. The total of watts used for each setting is 500 times the setting number. Write a function rule to describe the number of watts used for each setting. Find a reasonable domain and range for the function. Number of watts used is 500 times the setting #. watts f(x) = 500 x For each setting, the number of watts is f(x) = 500x watts.

33
Holt Algebra Writing Functions x f(x) (0) = 0 500(1) = (2) = 1, (3) = 1,500 There are 4 possible settings 0, 1, 2, and 3, so a reasonable domain would be {0, 1, 2, 3}. Check It Out! Example 5 Substitute these values into the function rule to find the range values. A reasonable range for this situation is {0, 500, 1,000, 1,500} watts.

34
Holt Algebra Writing Functions Lesson Quiz: Part I Identify the independent and dependent variables. Write a rule 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) = m

35
Holt Algebra Writing Functions Lesson Quiz: Part II Evaluate each function for the given input values. 4. For f(x) = 6x – 1, find f(x) when x = 3.5 and when x = –5. f(3.5) = 20 f(–5) = –31 3. For g(t) =, find g(t) when t = 20 and when t = –12. g(20) = 2 g(–12) = –6

36
Holt Algebra Writing Functions Lesson Quiz: Part III Write a function to describe the situation. Find a 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 Domain: {2, 3, 4} Range: {$500, $700, $900}

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google