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

2. Objectives Identify independent and dependent variables.
Write an equation in function notation
Evaluate a function for given input values.

3. Vocabulary independent variable dependent variable function rule
function notation

4. Input / Independent
Domain x
function
f(x) y
Range
Output / Dependent

5. The height of a candle depends on the # of hours it burns.
Identify the independent and dependent variables.
A painter must measure a room before deciding how much paint to buy.
The amount of paint depends 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 candle depends on the # of hours it burns.
Dependent: height of candle
Independent: # of hours

6. 3) A company charges $10 per hour to rent a jackhammer.
The cost to rent a jackhammer depends on the length of time it is rented.
Dependent variable: cost
Independent variable: time
4) Apples cost $0.99 per pound.
The cost of apples depends on the number of pounds bought.
Dependent variable: cost
Independent variable: pounds

7. Read as: f of x / function of x
Determine a relationship between the x- and y-values. x y 5 10 15 20 1 2 3 4
Step 1 List possible relationships between the first x and y
5 – 4 = or
10 – 4  2
Step 2 Write an equation. or
f(x) = (1/5)x
function notation
Read as: f of x / function of x

8. Read as: f of x / function of x
{(1, 3), (2, 6), (3, 9), (4, 12)} x 1 2 3 4 y 3 6 9 12
Step 1 List possible relationships between the first x and y
1  3 = or = 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

9. Identify the independent and dependent variables
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 is f(h) = 35h
A fitness center charges a $100 initiation fee plus $40 per month.
Dependent: total cost
Independent: number of months
Let m represent the number of months
The function is f(m) = 40m

10. You can think of a function as an input-output machine
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

11. WARM UP 1 2 3 4 5 6 Look at the pattern
1) Draw the 5th and the 6th figures.
2) Use the table to fill in the information
Figure no (x) 1 2 3 4 5 6
Square no(y)
3) Write an equation to show the relationship between x and y
4) How many squares will be used in the 20th figure?

12. Identify the independent and dependent variables
Identify the independent and dependent variables. Write an equation in function notation for the situation.
1) A math tutor charges $35 per hour.
Dependent: fee
Independent: hours y x
The function is y = 35x OR f(x) = 35x
2) A fitness center charges a $100 initiation fee plus $40 per month.
Dependent: total cost
Independent: number of months y x
The function is y = 40x OR f(x) = 40x + 100

13. Adnoc needed National day presents for their office staff
Adnoc needed National day presents for their office staff. The cost was 150 DHS per staff member present. They also had to pay 750 DHS to 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?

14. 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

15. Evaluate the function for the given input values.
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(7) + 2
= 3(–4) + 2 =
= –12 + 2
= 23
= –10

16. Evaluate the following expressions given the functions below:
g(x) = -3x f(x) = x h(x) = 12/x j(x) = 2x + 9
a) g(10)
b) f(3)
c) h(-2)
d) j(7)
e) h(-4)

17. The flu has spread throughout a town
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

18. 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) = m

19. 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

20. 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}