1. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Combining Functions ♦ Perform arithmetic operations on functions ♦ Perform composition of functions 5.1

2. Slide 5- 2 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Five Ways of Combining Two Functions f and g AdditionAddition SubtractionSubtraction MultiplicationMultiplication DivisionDivision CompositionComposition

3. Slide 5- 3 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Definition-Addition If f(x) and g(x) both exist, the sum, of two functions f and g are defined by

4. Slide 5- 4 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example of Addition of Functions: Let f(x) = x 2 + 2x and g(x) = 3x - 1

5. Slide 5- 5 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Definitions-Subtraction If f(x) and g(x) both exist, the difference of two functions f and g are defined by

6. Slide 5- 6 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example of Subtraction of Functions: Let f(x) = x 2 + 2x and g(x) = 3x  1

7. Slide 5- 7 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Examples of Evaluating Combinations of Functions – Using Symbolic Representations

8. Slide 5- 8 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Definitions-Multiplication If f(x) and g(x) both exist, the product of two functions f and g are defined by

9. Slide 5- 9 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example of Multiplication of Functions: Let f(x) = x 2 + 2x and g(x) = 3x  1

10. Slide 5- 10 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Definitions-Division If f(x) and g(x) both exist, quotient of two functions f and g are defined by

11. Slide 5- 11 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example of Division of Functions: Let f(x) = x 2 + 2x and g(x) = 3x  1 Find the symbolic representation for the function and use this to evaluateFind the symbolic representation for the function and use this to evaluate SoSo

12. Slide 5- 12 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Definitions-Composition If f(x) and g(x) both exist, the composition of two functions f and g are defined by

13. Composition of Functions-Symbolic Slide 5- 13 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Find a symbolic representation for the composite function g ○ f that converts x miles into inches.

14. Slide 5- 14 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example of Composition of Functions: Let f(x) = x 2 + 2x and g(x) = 3x – 1

15. Product and Composition of Two Functions Slide 5- 15 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

16. Slide 5- 16 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Evaluating Combinations of Functions Numerically Given numerical representations for f and g in the tableGiven numerical representations for f and g in the table Evaluate combinations of f and g as specified.Evaluate combinations of f and g as specified.

17. Slide 5- 17 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

18. Slide 5- 18 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Evaluating Combinations of Functions Graphically Use graph of f and g below to evaluateUse graph of f and g below to evaluate (f + g) (1)(f + g) (1) (f –g) (1)(f – g) (1) (f  g) (1)(f  g) (1) (f/g) (1)(f/g) (1) (f  g) (1)(f  g) (1) y = g(x) y = f(x)

19. Slide 5- 19 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley y = g(x) y = f(x)Answers: