Download 3.3 Notes Alg1.notebook

3.3 Notes Alg1.notebook
October 25, 2012
3­3 Writing Functions
Skills we've learned
1. Express the relation {(–2, 5), (–1, 4), (1, 3), (2, 4)} as a table, as a graph, and as a mapping diagram.
2. Give the domain and range of the graph:
Skills we need
3. Write an equation: "Cost of a book is $8 per book."
4. If f(x) = x + 2, what is f(3)?
Warm­up Answers
3. Write an equation: "Cost of a book is $8 per book."
4. If f(x) = x + 2, what is f(3)?
c = 8b
5
3.3 Notes Alg1.notebook
October 25, 2012
3­3 Writing Functions
1. Identify independent and dependent variables
2. Write an equation in function notation.
3. Evaluate using function notation.
Calculating how much money you will earn for working specific amounts of time.
I. Using a Table to Write an Equation
1. Determine a relationship between the x­ and y­values. Write an equation.
Step One
Possibilities:
Step Two
check for consistency:
Answer:
3.3 Notes Alg1.notebook
October 25, 2012
2. Determine a relationship between the x­ and y­values. Write an equation.
{(1, 3), (2, 6), (3, 9), (4, 12)}
Step One
1 • 3 = 3 or 1 + 2 = 3
Step Two
Answer
y = 3x
The value of y is 3 times x.
II. Identifying Independent & Dependent 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. Identify the independent and dependent variables in the situation.
3. 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 3.3 Notes Alg1.notebook
October 25, 2012
4. The height of a candle decreases d centimeters for every hour it burns.
Dependent: ___________
Independent: __________
5. A veterinarian must weigh an animal before determining the amount of medication. Dependent: ___________
Independent: __________
6. A company charges $10 per hour to rent a jackhammer.
Dependent: ___________
Independent: __________
7. Apples cost $0.99 per pound. Dependent: ___________
Independent: __________
III. Writing Functions
When an equation in two variables describes a function, you can use function notation to write it.
The dependent variable is a function of the independent variable. y is a function of x. y = f (x) y = f(x) 8. Identify the independent and dependent variables. Write an equation in function notation for the situation.
A math tutor charges $35 per hour. The fee a math tutor charges depends on number of hours. dependent: fee , Independent: hours
Let h represent the number of hours of tutoring. The function for the amount a math tutor charges is f(h) = 35h. 3.3 Notes Alg1.notebook
October 25, 2012
9. A fitness center charges a $100 initiation fee plus $40 per month. function:_____________
10. Steven buys lettuce that costs $1.69/lb. function:_____________
11. An amusement park charges a $6.00 parking fee plus $29.99 per person. function:_____________
V. Evaluating Functions 12. Evaluate the function for the given input values. For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4. f(x) = 3(x) + 2 f(x) = 3(x) + 2 Substitute 7 for x.
f(7) = 3(7) + 2 f(7) = 21 + 2 f(7) = 23 Substitute –4 for x.
f(–4) = 3(–4) + 2 f(–4) = ­12+ 2 f(–4) = ­10
3.3 Notes Alg1.notebook
October 25, 2012
V. Evaluating Functions 13. Evaluate the function g(t) = 1.5t – 5 when t = 6 and when t = –2.
g(t) = 1.5t – 5 g(t) = 1.5t – 5 g(6) = 1.5(6) – 5 = 9 – 5 = 4 g(–2) = 1.5(–2) – 5 = –3 – 5 = –8
VI. Finding the Reasonable Domain and Range
When a function describes a real­world 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. 14. Joe has enough money to buy 1, 2, or 3 DVDs at $15.00 each, if he buys any at all. a. Write a function to describe the situation. If Joe buys x DVDs, he will spend f(x) = 15x dollars. b. Find the reasonable domain of the function.
Joe only has enough money to purchase 1, 2, or 3 DVDs. A reasonable domain is {0, 1, 2, 3}. c. Find the reasonable range of the function.
Substitute the domain values into the function rule to find the range values. A reasonable range for this situation is {$0, $15, $30, $45}. 3.3 Notes Alg1.notebook
October 25, 2012
VI. Finding the Reasonable Domain and Range
15. The settings on a space heater are the whole numbers from 0 to 3. The total number of watts used for each setting is 500 times the setting number. a. Write a function to describe the situation. b. Find the reasonable domain of the function.
c. Find the reasonable range of the function.
3­3 p.183 #3 ­ 11 all, 12 ­ 27 (x3), 28, 30, 33 ­ 35 all