1. Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. MCS121 Calculus I Section 0.1 Functions

2. Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Definition 0.1.1 (p. 1)‏ Definition 0.1.2 (p. 2)‏ Calculus - the Study of Functions

3. Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Function Graphs

4. Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Definition 0.1.3 (p. 5) The Vertical Line Test

5. Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Figure 0.1.7 (p. 5) This curve cannot be the graph of a function.

6. Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Example- Absolute Value Function

7. Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Figure 0.1.12 (p. 7) The projection of y = f(x) on the x-axis is the set of allowable x-values for f, and the projection on the y-axis is the set of corresponding y-values. Domain and Range of a Function

8. Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Domain and Range of a Function Definition: The domain of y=f(x) is the set of all values of x for which f(x) is defined. The range is the set of corresponding y-values associated to the x domain values.

9. Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Find the natural domain and range of the function Ques tion 1 Example

10. Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Figure 0.1.17 (p. 9)‏ Example Let V be the volume of a box constructed as below. Find a formula for V(x). Find the domain of V.

11. Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Figure 0.1.17 (p. 9)‏

12. Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Class Practice