7-79 (Every fourth, and also 85; pp.192-193)

-.21. /(x) -1- 20 A. A function f is a rule that antigens to each element s in a set A 1(2). 1(-2). 5(1). f(a). f(-a). fa - 1) - clemeners) called /(s) in a set B. Which of the following tables defines y as a function of ? 22. M(x) = $3 + 4 1( 2 ). 1 - 2). h(@ ) . 1( - x ). "(a - 2). 1 (Vx) 23. (x ) -1+ 21 ((0). 1(3). 5(-3). 5(@). 5(-x).5 () 24. "( 1 ) - 1+ 4 : 6. Yes or No? If No, give a reason. Let f be a function. (a) Is it possible that f(1) - 5 and f(2) = 3? 1( - 1). 1(2). "(+). 1(x - 1 )." ( # ) (b) Is it possible that f( 1) - 5 and f(1) - 6? 25. 9(x) - SKILLS 9 ( 2 ) . 9 ( - 1 ) . 9 ( 2 ) . 9 ( a). 9(a - 1).9(x2 - 1) 7-10 = Function Notation Express the rule in function nota- tion. (For example, the rule "square, then subtract 5" is expressed 26. 9(1) = 1+ 2 the function f(x) = x2 - 5.) 7. Multiply by 3, then subtract 5-/(x) = 3x - 5 g(-2), g(2), 9(0), g(a), 9(a2 - 2), 9(a + 1) &. Square, then add 2 (27. ) k (x ) = -x2 - 2x + 3; 9. Subtract 1, then square k ( 0 ) , k ( 2 ) , k ( - 2 ), k ( V2 ) , k(a + 2 ), k ( - x), k(x 2 ) 10. Add 1, take the square root, then divide by 6 28. k (x ) = 2x3 - 3x2; 11-14 = Functions in Words Express the function (or rule) in * ( 0 ) , k ( 3 ) , k ( - 3), k (2 ), k(2), k ( - x), k(x3) words. multiply b2, chen add 3 29 . f ( x ) = 2/x - 1 1 ; (11. /(x) = 2x + 3 12. g (x ) =*+ 2 f ( - 2 ) , f (0 ), f ( 2 ), f ( 2 ) , f ( x + 1 ) , f ( x 2 + 2 ) 30 . f ( x ) = 1* 13. h(x) = 5(x + 1 ) 14 : k ( x ) = * - 4 15-16 - Machine Diagram Draw a machine diagram for the f ( - 2 ) , f ( - 1 ) , f(0 ) , $(5 ) , f ( x 2 ) , f ( * ) function. 15. f ( x ) = Vx- I 16. f (x) = - 31-34 . Piecewise Defined Functions Evaluate the piecewise - 2 defined function at the indicated values. 17-18 - Table of Values Complete the table. 1 31 . f( x ) = x if x 2 - 1 - ON W f ( - 3 ) , f(0 ) , f( 2 ) , f ( 3 ) , f ( 5 ) WN - (x2 + 2x ifx 5 - 1 33. f(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 ) (19, f(x ) = x2 - 6; $(-3), $(3 ), $10 ), f( ) 3 x if x 2 f ( - 5 ) , f(0 ) , f( 1 ) , f ( 2 ) , f ( 5 )SECTION 2.1 = Functions 193 73-76 = Four Ways to Represent a Function A ver in A verbal descrip- 35-38 = Evaluating Functions Use the function to evaluate the tion of a function is given. Find (a) algebraic, (b) numerical, and the indicated expressions and simplify. (c) graphical representations for the function. (35. ) 1(x) - 23 + 1: 10 + 21. 1(1 ) + 1(2) .73. To evaluate J(x), divide the input by 3 and add } to the result. 36. J(x) = 3x - 1: 1(2x). 25(x) 74. To evaluate g(x), subtract 4 from the input and multiply the 37. J(x) - *+4: 5(:").((x)' result by 1. Let 7(x) be the amount of sales tax charged in Lemon 38. /(x) - or - 18: (;).49 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 76. Let V(d) be the volume of a sphere of diameter d. To find the function between the given inputs. volume, take the cube of the diameter, then multiply by or (39. /f(x) - 3x - 2; from I to 5 and divide by 6. 40. f(x) - 4 - 5x; from 3 to 5 41. 9(1) - 1 - 12; from -2 to 5 SKILLS Plus 42. h(t) = 1 + 5; from -3 to 6 77-78 = Domain and Range Find the domain and range of f. 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 J(a + h) -J(a where h # 0 78. f ( x ) = 3 if x is rational 5x if x is irrational (.43. 1 ( x ) = 5 - 2x 44. f(x) = 3x2 + 2 45. f( x ) = 5 46. f (x) = - 1 smainl APPLICATIONS 47. f (x) =* 48. f(x) = - 2x 79. Torricelli's Law A tank holds 50 gal of water, which drains from a leak at the bottom, causing the tank to empty in 20 min. The tank drains faster when it is nearly full because 49. f (x ) = 3 - 5x + 4x2 50. f (x ) = x3 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 (t ) = 50( 1 20 ) Ost= 20 151, f ( x ) = 3x 2 52. f(x) = 5x2+ 4 01203.8 (a) Find V(0) and V(20). 53 . f ( x ) = 3x , - 25x56 54 . f ( x ) = 5x2 +4, 05x52 ei T leos Islot sdT . esla b) What do your answers to part (a) represent? avela leong s sort 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 55-72 - Domain Find the domain of the function. 0 min to 20 min. * / 55. f(x ) - 56. f (x) = to noilonut s es 3 as terd slurmot sdT 3x - 6 uibe thiew vishis x 4 mo ni) 2 function (b) Find T(2), T(3), and T(5). v(r) = 18,500(0.25 -12) Our= 0.5 (c) What do your answers in part (b) represent? (a) Find v(0.1) and v(0.4). 88. Speeding Tickets In a certain state the maximum speed per- (b) What do your answers to part (a) tell you about the flow of blood in this artery? mitted on freeways is 65 mi/h, and the minimum is 40 mi/h. The fine F for violating these limits is $15 for every mile (c) Make a table of values of v( r) for r = 0, 0.1, 0.2, 0.3, 0.4, 0.5. above the maximum or below the minimum. (a) Complete the expressions in the following piecewise (d) Find the net change in the velocity v as r changes from 0.1 cm to 0.5 cm. defined function, where x is the speed at which you are driving. siadq2 1 10 GerA .08 yd novig a eviben ali to doit if 0 65 (b) Find F(30), F(50), and F(75). (c) What do your answers in part (b) represent