### 3.1 Functions Notes and CW 15 HW 15: P. 108 #1

```Name _________________________________________________________
3.1
Date __________
Functions Notes and CW 15
HW 15: P. 108 #1-21 odds
A relation pairs inputs with outputs. A function is a relation that pairs each input with exactly one output.
The domain of a function is the set of all possible input values. The variable that represents the input values of a function
is the independent variable.
The range of a function is the set of all possible output values. The variable that represents the output values of a function
is the dependent variable.
Vertical Line Test
Words A graph represent a function when no vertical line passes through more than one point on the
graph.
Examples Function
Not a function
In Exercises 1 and 2, determine whether the graph represents a function. Explain.
1.
2.
In Exercises 3 and 4, find the domain and range of the function represented by the graph.
3.
4.
Algebra 1
Student Journal
61
In Exercises 5 and 6, determine whether the relation is a function. Explain.
5.
Input, x
–2
0
1
–2
Output, y
4
5
4
5
6.
(0, 3), (1, 1), (2, 1), (3, 0)
7. The function y = 12 x represents the number y of pages of text a computer printer can print in x minutes.
a. Identify the independent and dependent variables.
b. The domain is 1, 2, 3, and 4. What is the range?
CW 15 What Has A Foot On Each End And One In The Middle?
Write the letter of each answer in the box containing the exercise number.
Determine whether the relation is a function.
1. (8, 5,
2. ( 2, − 3), (3, 2), ( 4, 7), (5, 14), (6, 23)
) (6, − 2), (4, − 9), (2, − 6), (4, 7)
H. yes
3.
I. no
(−11, 2), (− 9, 2), (− 7, 3), (− 5, 3), (− 3, 3)
A. yes
5.
A. yes
4.
B. no
(1, − 4), (2, 1), (3, 4), (3, 3), (4, 2)
B. yes
(17, − 3), (2, − 2), (1, 1), (2, 2), (17, 3)
C. yes
B. no
6.
D. no
C. no
(− 4, 12), (1, 6), (4, − 2), (7, − 8), (10, −14)
K. yes
L. no
Find the domain and range of the function represented by the graph.
7.
8.
T. D: − 2 ≤ x ≤ 2
S. D: 0 ≤ x ≤ 4
R: − 2 ≤ y ≤ 2
Q. D: 0 ≤ x ≤ 3
R. D: 0 < x ≤ 3
R: 0 ≤ y ≤ 3
R: 0 < y ≤ 3
R: 0 ≤ y ≤ 4
Use the following information to answer Exercises 9 and 10. The function t =− 8 j + 24 represents the
number of tomatoes t that your neighbor has left after making j jars of homemade salsa.
9. Identify the dependent variable.
R. jars of salsa
S. tomatoes
3
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Algebra 1
Student Journal
10. Identify the independent variable.
10
2
8
Y. jars of salsa
5
9
7
1
4
Z. tomatoes
6