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Section 10.1

Section 10.1. The Algebra of Functions. Chapter 10. Section 10.1 Exercise #1. Chapter 10. Section 10.1 Exercise #3. Chapter 10. Section 10.1 Exercise #4. Find the sum, difference, product, and quotient of two functions. A. OBJECTIVES. Find the composite of two functions. B. OBJECTIVES.

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Section 10.1

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  1. Section 10.1 The Algebra of Functions

  2. Chapter 10 Section 10.1Exercise #1

  3. Chapter 10 Section 10.1Exercise #3

  4. Chapter 10 Section 10.1Exercise #4

  5. Find the sum, difference, product, and quotient of two functions. A OBJECTIVES

  6. Find the composite of two functions. B OBJECTIVES

  7. Find the domain of (ƒ + g)(x), (ƒ – g)(x), (ƒg)(x), and C OBJECTIVES

  8. Solve an application. D OBJECTIVES

  9. DEFINITION OPERATIONS WITH FUNCTIONS

  10. DEFINITION COMPOSITE FUNCTION If ƒ and g are functions:

  11. Section 10.2 Inverse Functions

  12. Find the inverse of a function when the function is given as a set of ordered pairs. A OBJECTIVES

  13. Find the equation of the inverse of a function. B OBJECTIVES

  14. Graph a function and its inverse and determine whether the inverse is a function. C OBJECTIVES

  15. Solve applications involving functions. D OBJECTIVES

  16. DEFINITION INVERSE OF A FUNCTION The relation obtained by reversing the order of x and y.

  17. PROCEDURE FINDING THE EQUATION OF AN INVERSE FUNCTION Interchange the roles of x and y. Solve for y.

  18. DEFINITION If y = ƒ(x) is one-to-one, the inverse of ƒ is also a function, denoted by y = ƒ –1(x).

  19. Chapter 10 Section 10.2Exercise #6

  20. Chapter 10 Section 10.2Exercise #8

  21. The inverse is not a function.

  22. Section 10.3 Exponential Functions

  23. Graph exponential functions of the form ax or a –x (a > 0). A OBJECTIVES

  24. Determine whether an exponential function is increasing or decreasing. B OBJECTIVES

  25. Solve applications involving exponential functions. C OBJECTIVES

  26. DEFINITION EXPONENTIAL FUNCTION A function defined for all real values of x by:

  27. DEFINITION INCREASING AND DECREASING FUNCTIONS Increasing: rises left to right. Decreasing: falls left to right.

  28. DEFINITION NATURAL EXPONENTIAL FUNCTION, BASE e

  29. Chapter 10 Section 10.3Exercise #9

  30. y x Yes

  31. increasing

  32. Chapter 10 Section 10.3Exercise #10

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