1. PreCalculus 3-R Unit 3 Functions and Graphs

2. Review Problems Evaluate the function f (x) = x 2 + 6x at f (8). f (8) = 112 Evaluate the function at f (6). f (6) = 28 1

3. Review Problems Evaluate the following piecewise defined function at f (1), f (3), and f (7). f (1) = 1, f (3) = 18, f (7) = 50 Determine whether the equation defines y as a function of x Yes 2

4. Review Problems Use the function f (x) = x 2 + 1 to evaluate the following expressions and simplify. f (x + 5) and f (x) + f (5) For the function, find. 3

5. Review Problems What is the domain of the function  What is the domain of the function 4

6. Review Problems Sketch the graph of the piecewise defined function 5

7. Review Problems Sketch the graph of the piecewise defined function 6

8. Review Problems Sketch the graph of the piecewise defined function 7

9. Review Problems Determine whether the equation defines y as a function of x. No Consider a family of functions. How does the value of c affect the graph? The graphs are obtained by shifting the graph of upward c units, 8

10. Review Problems The graph of g is given. Sketch the graph of the function 9

11. Review Problems The function f (x) is reflected in the x-axis and then shifted up 5 units and the graph of g (x) = 5 – x 2 is obtained. What is f (x)? f (x) = x 2 10

12. Review Problems The graph of f is given. Sketch the graph of the function y = –f(x) + 3. 11

13. Review Problems Express the function in the form Find the inverse function of 12

14. Review Problems Use the given graphs of f and g to evaluate g (f (5)). 3 13

15. Review Problems For find Find the inverse function of 14

16. Review Problems A function f is given. Sketch the graph of f. Use the graph of f to sketch the graph of. Find 15

17. Review Problems Assume f is a one-to-one function. If f (x) = 3 – 6x, find f –1 (33). –5 Use the Property of Inverse Functions to find the inverse function of f(x) = x + 8 f –1 (x) = x – 8 16

18. Review Problems Find the inverse function of 17

19. Review Problems Express the function in the form evaluate f(g(–1)). -2 18

20. Review Problems Use the given graphs of f and g to evaluate g (f (5)) 3 19

21. Review Problems Find the domain of Suppose that g(x) = 5x + 3 and h(x) = 25x 2 + 30x + 19. Find a function f, such that f(g(x)) = h(x). f(x) = x 2 + 10 20

22. Review Problems A function f is given Sketch the graph of f. Use the graph of f to sketch the graph of. Find 21

23. Review Problems A one-to-one function is given Find the inverse of the function. Graph both the function and its inverse on the same screen to verify that the graphs are reflections of each other in the line y=x. 22

24. Review Problems A one-to-one function is given Find the inverse of the function. Graph both the function and its inverse on the same screen to verify that the graphs are reflections of each other in the line y=x. 23

25. Review Problems Assume f is a one-to-one function. If f (x) = 3 – 6x, find f –1 (33). -5 Use the Property of Inverse Functions to find the inverse function of f(x) = x + 8. f –1 (x) = x – 8 24

26. Review Problems Find the inverse function of 25

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35. Review Problems 34

36. Answers 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. f (8) = 112 f (6) = 28 f (1) = 1, f (3) = 18, f (7) = 50 Yes No The graphs are obtained by shifting the graph of upward c units, f (x) = x 2 3

37. Answers 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. –5 f –1 (x) = x – 8 -2 3 f(x) = x 2 + 10 -5 f –1 (x) = x – 8

38. Answers 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.