SPARKPOINT CCSp option rvices for Students & mmunity 192 CHAPTER 2 .. Functions 5. A function / is a rule that assigns to each element : in a set A 1(2). 5(-2). 1(1). 5(a). 5(-a). f(a - 1) -clement(s) called /(x) in a set 89. Which of the following tables defines y as a function of "? 22. "(x ) = 4 + 4 (1) "(2). 11(-2). 1(@), 11(-* ). 11(0 - 2).1 ( Vx ) 23. ( x )=x+ 2x1 (0). 5(3). 5( - 3), 5 ( a). 5(-x).5 ( a) En CCSE 24 . 1 ( 1 ) = 14 4: 6. Yes or No? If No. give a reason. Let f be a function. Course: (a) Is it possible that f(1) = 5 and f(2) = 5? " ( - 1 ), h ( 2), " ( 2). 1(x - 1). "(# ) (b) Is it possible that f( 1) = 5 and f( 1) = 6? Units: 5 25 . 9 ( * ) = 1+x Semester SKILLS 9 ( 2), 9 ( - 1), 9(2), 9(a), g(a - 1), 9(x2 - 1) 7-10 = Function Notation Express the rule in function nota- Dates: 08 tion. (For example, the rule "square, then subtract 5" is expressed 26. g(1) = _ - 1 - 2' as the function f(x) = x2 - 5.) g( -2), 9(2), 9(0), g(a), g(a2 - 2), 9(a + 1) CRN: 72 7. Multiply by 3, then subtract 5-7/( x) = 3x - 5 Square, then add 2 27 . k ( x ) = - x 2 - 2x + 3 ; Days: TF 9. Subtract 1, then square k ( 0 ) , k ( 2 ) , k ( - 2 ) , k ( V2 ), k (a + 2 ), k ( - x ) , k (xx2 ) 10. Add 1, take the square root, then divide by 6 28. k (x ) = 2x3 - 3x2; Time: 11:1 11-14 = Functions in Words Express the function (or rule) in k (0 ), k ( 3 ), k ( - 3 ), k (2 ), k(2 ), k (-x), k(x3) Office Hou words. multiply b2, then add 3 29. f(x) = 21x- 11; (11. ((x) = 2 +3-7" 12 . g ( x ) = * + 2 f ( - 2), f (0 ), f ( 2), f(2), f( x + 1 ), f(x2 + 2) 1 a aaudia Office Hou 3 30 . f ( x ) = 1 13. h(x) = 5(x + 1) 14: k (x ) = * - 4 ethod of 3 vas 15-16 - Machine Diagram Draw a machine diagram for the f ( - 2 ) , f ( - 1 ) , f (0 ) , f ( 5 ) , f ( * 2 ) , f ( ) function. ning M (5 f(x ) = Vx - I 16. f (x ) = - 31-34 - Piecewise Defined Functions Evaluate the piecewise x - 2 defined function at the indicated values. 17-18 - Table of Values Complete the table. if x ront P 17. f (x ) = 2(x - 1)2 18. g(x) = | 2x + 3 / A . emer f ( - 2 ) , f ( - 1 ), f(0 ) , f(1 ) , f ( 2 ) f(x) g(x) IS, 32 . f ( x ) = 15 if x = 2 ts; (2x - 3 ifx > 2 at senado Jon art (3) f ( - 3 ), f(0 ) , f (2 ), f (3 ) , f (5 ) WN HO - ON (x2 + 2x ifx 5 - 1 33. f(x) = x if - 1 1 19-30 Evaluating Functions Evaluate the function at the indicated values. f ( - 4 ), f ( - 2 ), f ( - 1 ), f(0 ), f( 25 ) 3x (19, f ( x ) = x 2 - 6 ; f(- 3 ), f (3 ) , f(0 ) , f ( 2 ) if x 2 f ( - 5 ), f(0 ), f (1 ) , f ( 2 ), f( 5 )SECTION 2.1 . Functions 193 35-38 = Evaluating Functions Use the fun metion A verbal descrip indicated expressions and simplify. 73-76 . Four Ways to Represent a Females (by numerical, and Been ed a function is gives tationus for the function. 36. f(x) - 3x - 1: 1(2:).25() ".71. To evaluate /(s), divide the input by 3 and add ; to the result 37. 5(x) - 2+4 50:").(10)) 74. To evaluate o(). subtract 4 from the input and multiply the result by 1. 38. J(x) - ex - 18: 5( ;). 50 Let T(x) be the amount of sales tax charged in Lemon County on a purchase of & dollars. To find the tax, take 8% of the purchase price. 39-42 = Net Change Find the net change in the value of the function between the given inputs. 76. Let V(d) be the volume of a sphere of diameter d. To find the volume, take the cube of the diameter, then multiply by or (39. /f(x) - 3x - 2: from 1 to 5 and divide by 6. 40. f(x) - 4 - 5x: from 3 to 5 41. 9(1) = 1 -1: from -2 to 5 SKILLS Plus 42. h(1) = 12 + 5: from -3 to 6 77-78 = Domain and Range Find the domain and range of J. if x is rational 43-50 = Difference Quotient Find f(a), f(a + h), and the 77. f(x ) = if x is irrational difference quotient f(a + h) - fa) where h 0. 78. f (x ) =1 if x is rational ( 43. 1(x) = 5 - 2x 5x if x is irrational 44. f (x) = 3x2 + 2 45. f ( x ) = 5 46. f(x) = x + 1 APPLICATIONS 79. Torricelli's Law A tank holds 50 gal of water, which drains 47. f ( x ) = x + 1 48. f ( x ) = - 2x from a leak at the bottom, causing the tank to empty in x - 1 orir to 20 min. The tank drains faster when it is nearly full because 49. f (x ) = 3 - 5x+ 4x2 50 . f ( x ) = x ONS the pressure on the leak is greater. Torricelli's Law gives the volume of water remaining in the tank after t minutes as 51-54 = Domain and Range Find the domain and range of the function. V(1 ) = 50( 1 - 20) ost= 20 51, f ( x ) = 3x 52. f(x ) = 5x2 + 4030 (a) Find V(0) and V(20). 53 . f ( x ) = 3x , - 25 x=6 (b) What do your answers to part (a) represent? 54 . f ( x ) = 5x2 + 4 , 05x52 (c) Make a table of values of V(t) for t = 0, 5, 10, 15, 20. (d) Find the net change in the volume V as t changes from 0 min to 20 min. 55-72 - Domain Find the domain of the function. phing Function g tardi slurmot sdT ( 55. f( x ) = x - 3 56. f(x ) = nimal to 3x - 6 unction f, we plot guidepoit die (r, y) whose 57 . f ( x ) = *+ 2 58. f ( x ) - 72 + x - 6 "@jput of the fur ( 59. f (t ) = Vi+ In orly augle 60. g(t) = V +2 + 9 61. f (t) = Vt - 1 62. 9(x) = V7 - 3x 63. f(x) = V1 -2x nimrod 64. 9(x) = Vx2 -4 V2 + x lol all 1 Vx 65. g(x) = - 3 - * 66. 9(x) = 2x2 + x- 1 67. /9(x) = Vx2 - 6x 68. g(x) = Vx2 - 2x -8 80. Area of a Sphere The surface area S of a sphere is a func- * 2 tion of its radius r given by 69. f (x) = - 3 70. f(x ) = - Vx - 4 V6 - x S ( r ) = 4 Tr 2 ( x + 1)2 x (a) Find S(2) and S(3). 71. f(x) (20) 72. f ( x ) = V2x - V9 -: (b) What do your answers in part (a) represent