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. Copyright © Big Ideas Learning, LLC All rights reserved. 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 62 Algebra 1 Student Journal 10. Identify the independent variable. 10 2 8 Y. jars of salsa 5 9 7 1 4 Z. tomatoes 6 Copyright © Big Ideas Learning, LLC All rights reserved. Copyright © Big Ideas Learning, LLC All rights reserved. Algebra 1 Student Journal 63