1. Section 1 Chapter 11

2. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 2 Additional Graphs of Functions 11.1 Recognize the graphs of the elementary functions defined by |x|, and and graph their translations. Recognize and graph step functions.

3. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Recognize the graphs of the elementary functions defined by |x|, and and graph their translations. Objective 1 Slide 11.1- 3

4. Copyright © 2012, 2008, 2004 Pearson Education, Inc. The elementary function defined by f(x) = |x| is called the absolute value function. Domain: ( ,  ) Range: [0,  ) Slide 11.1- 4 Recognize the graphs of the elementary functions defined by and and graph their translation.

5. Copyright © 2012, 2008, 2004 Pearson Education, Inc. The reciprocal function, defined by f(x) = 1/x, is a rational function. The axes are asymptotes for the function. Domain and Range are both ( , 0)  (0,  ). Slide 11.1- 5 Recognize the graphs of the elementary functions defined by and and graph their translation.

6. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Recognize the graphs of the elementary functions defined by and and graph their translation. The square root function, defined by We restrict the function values to be real numbers, x cannot take on negative values. Domain: [0,  ) Range: [0,  ) Slide 11.1- 6

7. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Graph Give the domain and range. The graph is found by shifting the graph of the square root function, 4 units to the left. The domain is [  4,  ). The range is [0,  ). Slide 11.1- 7 CLASSROOM EXAMPLE 1 Applying a Horizontal Shift Solution:

8. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Graph Give the domain and range. The graph is found by shifting the graph of the reciprocal function 2 units down. Since x ≠ 0, the line x = 0 is a vertical asymptote. The domain is ( , 0)  (0,  ). The line y = –2 is a horizontal asymptote. The range is ( ,  2)  (  2,  ). Slide 11.1- 8 CLASSROOM EXAMPLE 2 Applying a Vertical Shift Solution:

9. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Graph Table of values. x1/xy 22  1/2  5/2 11 11 33  1/2 22 44 1/220 11 11 2  3/2 Slide 11.1- 9 CLASSROOM EXAMPLE 2 Applying a Vertical Shift (cont’d)

10. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Graph Give the domain and range. The graph is shifted 2 units left and 1 unit up. The domain is ( ,  ). The range is [1,  ). xy 44 3 33 2 22 1 11 2 03 Slide 11.1- 10 CLASSROOM EXAMPLE 3 Applying Both Horizontal and Vertical Shifts Solution:

11. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Recognize and graph step functions. Objective 2 Slide 11.1- 11

12. Copyright © 2012, 2008, 2004 Pearson Education, Inc. The greatest integer function, written pairs every real number x with the greatest integer less than or equal to x. Slide 11.1- 12 Recognize and graph step functions.

13. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Evaluate each expression. Slide 11.1- 13 CLASSROOM EXAMPLE 4 Finding the Greatest Integer Solution:

14. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Graph Give the domain and range. The domain is ( ,  ). The range is the set of integers {…,  2,  1, 0, 1, 2, …}. [ ) [ ) [ ) [ ) [ ) Slide 11.1- 14 CLASSROOM EXAMPLE 5 Graphing the Greatest Integer Function Solution:

15. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Assume that the post office charges 80 cents per oz (or fraction of an ounce) to mail a letter to Europe. Graph the ordered pairs (ounces, cost) in the interval (0, 4]. This function is similar to the greatest integer function, but in this case, we use the integer that is greater than or equal to the number. Slide 11.1- 15 CLASSROOM EXAMPLE 6 Applying a Greatest Integer Function Solution:

16. Copyright © 2012, 2008, 2004 Pearson Education, Inc. (] (] (] (] Slide 11.1- 16 CLASSROOM EXAMPLE 6 Applying a Greatest Integer Function (cont’d)