1. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 1 Start-Up Day 3

2. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 2 Objective: Students will be able to identify the graphs of the twelve basic functions and investigate the domain, continuity, symmetry and asymptotes of each. Essential Question: What are the parent graphs and general characteristics of the 12 basic functions? Home Learning: p. 106 #1-12, 34, 35, 41 & 45

3. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 3 1.3 Twelve Basic Functions Demana, Waits, Foley, Kennedy

4. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 4 What you’ll learn about  What Graphs can Tell Us  Twelve Basic Functions  Analyzing Functions Graphically … and why As you continue to study mathematics, you will find that the twelve basic functions presented here will come up again and again. By knowing their basic properties, you will recognize them when you see them.

5. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 5 The Identity Function

6. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 6 The Squaring Function

7. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 7 The Cubing Function

8. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 8 The Reciprocal Function

9. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 9 The Square Root Function

10. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 10 The Exponential Function

11. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 11 The Natural Logarithm Function

12. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 12 The Sine Function

13. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 13 The Cosine Function

14. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 14 The Absolute Value Function

15. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 15 The Greatest Integer Function

16. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 16 The Logistic Function

17. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 17 Example: Looking for Domains One of the functions has domain the set of all reals except 0. Which function is it?

18. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 18 Solution One of the functions has domain the set of all reals except 0. Which function is it?

19. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 19 Example: Analyzing a Function Graphically

20. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 20 Solution