Transcription of Definition of a Function and Evaluating a Function Domain ...
1 SECTION An Introduction to functions MATH 1330 precalculus 1 Chapter 1 A Review of functions Section : An Introduction to functions Definition of a Function and Evaluating a Function Domain and Range of a Function Definition of a Function and Evaluating a Function Definition : CHAPTER 1 A Review of functions University of Houston Department of Mathematics 2 Defining a Function by an Equation in the Variables x and y: Example: Solution: The Function Notation: SECTION An Introduction to functions MATH 1330 precalculus 3 Evaluating a Function : Example: Solution: CHAPTER 1 A Review of functions University of Houston Department of Mathematics 4 Example: Solution: SECTION An Introduction to functions MATH 1330 precalculus 5 Difference Quotients: Example: Solution: Additional Example 1: Solution: CHAPTER 1 A Review of functions University of Houston Department of Mathematics 6 Additional Example 2: Solution: Additional Example 3: SECTION An Introduction to functions MATH 1330 precalculus 7 Solution: Additional Example 4: Solution: CHAPTER 1 A Review of functions University of Houston Department of Mathematics 8 Additional Example 5: Solution: SECTION An Introduction to functions MATH 1330 precalculus 9 Additional Example 6: Solution: CHAPTER 1 A Review of functions University of Houston Department of Mathematics 10 Additional Example 7: Solution: Domain and Range of a Function Review of Interval Notation.
2 SECTION An Introduction to functions MATH 1330 precalculus 11 Finding the Domain of a Function : Example: Solution: CHAPTER 1 A Review of functions University of Houston Department of Mathematics 12 Example: Solution: Finding the Range of a Function : SECTION An Introduction to functions MATH 1330 precalculus 13 Example: Solution: Additional Example 1: Solution: CHAPTER 1 A Review of functions University of Houston Department of Mathematics 14 Additional Example 2: Solution: Additional Example 3: Solution: SECTION An Introduction to functions MATH 1330 precalculus 15 Additional Example 4: Solution: Additional Example 5: Solution: CHAPTER 1 A Review of functions University of Houston Department of Mathematics 16 SECTION An Introduction to functions MATH 1330 precalculus 17 CHAPTER 1 A Review of functions University of Houston Department of Mathematics 18 Additional Example 6: Solution: Additional Example 7: Solution: SECTION An Introduction to functions MATH 1330 precalculus 19 Exercise Set : An Introduction to functions University of Houston Department of Mathematics 20 For each of the examples below, determine whether the mapping makes sense within the context of the given situation, and then state whether or not the mapping represents a Function .
3 1. Erik conducts a science experiment and maps the temperature outside his kitchen window at various times during the morning. 2. Dr. Kim counts the number of people in attendance at various times during his lecture this afternoon. State whether or not each of the following mappings represents a Function . If a mapping is a Function , then identify its Domain and range. 3. 4. 5. 6. Express each of the following rules in Function notation. (For example, Subtract 3, then square would be written as2)3()( xxf.) 7. Divide by 7, then add 4 8. Multiply by 2, then square 9. Take the square root, then subtract 6 10. Add 4, square, then subtract 2 Find the Domain of each of the following functions . Then express your answer in interval notation. 11. 35)( xxf 12. 16)( xxxf 13. 94)(2 xxxg 14. 413)(2 xxxf 15. 281156)(22 xxxxxf 16.
4 208153)(2 xxxxg 17. ttf )( 18. 3)(xxh 19. 5)(xxg 20. 4)(tth 21. 5)( xxf 22. 7)( xxg 23. 423)( xxxF 24. 73)( xxxG A B 7 9 -3 0 5 4 A B 0 8 4 2 A B -2 9 -6 1 A B 9 -6 8 4 -7 9 10 57 62 65 Time Temp. (oF) Time 1 2 3 85 87 # of People Exercise Set : An Introduction to functions MATH 1330 precalculus 21 25. 35)( xxf 26. 326)( xxxg 27. 32587)( tttth 28. 57492)( xxxf 29. 2( )1024f ttt 30. 145)(2 tttg Find the Domain and range of each of the following functions . Express answers in interval notation. 31. (a) ()f xx (b) ( )6g xx (c) ( )6h xx (d) ( )6 3p xx 32. (a) ( )3f tt (b) ( ) 3g tt (c) ( )3h tt (d) ( )37p tt 33. (a) 2( )4f xx (b) 2( )4g xx (c) 2( )4h xx (d) 2( )4p xx (e) 2( )4q xx (f) 2( )4r xx 34. (a) 2( ) 25f tt (b) 2( )25g tt (c) 2( )25h tt (d) 2( )25p tt (e) 2( )25q tt (f) 2( )25r tt 35.
5 (a) ()f tt (b) ( )9g tt (c) ( ) 9h tt 36. (a) ()f xx (b) ( )1g xx (c) ( )1h xx 37. (a) 2( )3f xx (b) 2( )34g xx (c) 2( )235h xx 38. (a) 2( )6f tt (b) 2( )67g tt (c) 213( )68h tt 39. ( )275g tx 40. ( )61h tt 41. 3( )56 4f xx 42. 4( )8 32g xx Find the Domain and range of each of the following functions . Express answers in interval notation. (Hint: When finding the range, first solve for x.) 43. (a) 3()2fxx (b) 5()2xgxx 44. (a) 4()3fxx (b) 52()3xgxx Exercise Set : An Introduction to functions University of Houston Department of Mathematics 22 Evaluate the following. 45. If 45)( xxf, find: )3()(,3)(),3(),(,),3(21fafafafafff 46. If 13)( xxf, find: )2()(),2(,2)(,),8(),5(74ftftftffff 47. If 43)(2 xxxg, find: )(3),3(,),5(,),0(141agaggxggga 48.
6 If 52)(2 ttth, find: )(2),2(),(),6(,),1(23xhxhxhchhh 49. If 32)( xxxf, find: )3(),(,),0(),7(253 tftffff 50. If xxxxf 4)(2, find: 2)(),3(,),5(),2(347 pfpffff 51. If 4 if,34 if,52)(2xxxxxf, find: 29),4(),0(,3),2(),6(ffffff 52. If 2 if,272 if,4)(2xxxxxxf, find: 310),2(),1(,0),3(),5( ffffff 53. If 2 if,52x0 if,40 if,3)(2xxxxxf, find: 23),4(),1(,2),6(),0(ffffff 54. If 3 if,73x1- if,61 if,74)(2xxxxxf, find: 35),6(),3(,1),4(),0( ffffff Determine whether each of the following equations defines y as a Function of x. (Do not graph.) 55. 853 yx 56. 23yx 57. 32 yx 58. xxyx5234 59. 574 yx 60. 16322 yx 61. 623 yyx 62. 53 yx 63. yx53 64. xy73 65. 2yx 66. 34xy Exercise Set : An Introduction to functions MATH 1330 precalculus 23 For each of the following problems: (a) Find ()f x h . (b) Find the difference quotient ()( )f x hf xh.
7 (Assume that 0h .) 67. 47)( xxf 68. xxf35)( 69. 25)(2 xxxf 70. 83)(2 xxxf 71. 8)( xf 72. 6)( xf 73. 1fxx 74. 13fxx
