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. Example 1: Using a Table to Write an Equation
Determine a relationship between the x- and y-values. Write an equation. x y 5 10 15 20 1 2 3 4
Step 1 List possible relationships between the first x or y-values.
5 – 4 = 1 or

3. Example 1 Continued
Step 2 Determine if one relationship works for the remaining values.
10 – 4  and
15 – 4  and
20 – 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.

4. 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 1 2 3 4 y 3 6 9 12
Step 1 List possible relationships between the first x- or y-values.
1  3 = 3 or = 3

5. Check It Out! Example 1 Continued
Step 2 Determine if one relationship works for the remaining values.
2 • 3 = 6
3 • 3 = 9
4 • 3 = 12
2 + 2  6
3 + 2  9
4 + 2  12
The value of y is 3 times x.
Step 3 Write an equation.
y = 3x
The value of y is 3 times x.

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

7. 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

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

9. Helpful Hint
There are several different ways to describe the variables of a function.
Independent
Variable
Dependent
Variable
x-values
y-values
Domain
Range
Input
Output x
f(x)

10. Check It Out! Example 2a
Identify the independent and dependent variable in the situation.
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

11. Check It Out! Example 2b
Identify the independent and dependent variable in the situation.
Apples cost $0.99 per pound.
The cost of apples depends on the number of pounds bought.
Dependent variable: cost
Independent variable: pounds

12. 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(x) = 3(x) + 2
f(x) = 3(x) + 2
Substitute
7 for x.
Substitute
–4 for x.
f(7) = 3(7) + 2
f(–4) = 3(–4) + 2 =
Simplify.
Simplify.
= –12 + 2
= 23
= –10

13. 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(t) = 1.5t – 5
g(6) = 1.5(6) – 5
g(–2) = 1.5(–2) – 5
= 9 – 5
= –3 – 5
= 4
= –8

14. 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

15. 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(c) = 2c – 1
h(1) = 2(1) – 1
h(–3) = 2(–3) – 1
= 2 – 1
= –6 – 1
= 1
= –7

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

17. 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}