Problem 1E: If f(x) = x3 + 1, then (a) the value of f at x = 1 is f(_____) = __________. (b) the value of f at x... Problem 2E: For a function f, the set of all possible inputs is called the __________ of f, and the set of all... Problem 3E: (a) Which of the following functions have 5 in their domain? f(x)=x23xg(x)=x5xh(x)=x10 (b) For the... Problem 4E: A function is given algebraically by the formula f(x) = (x 4)2 + 3. Complete these other ways to... Problem 5E: A function f is a rule that assigns to each element x in a set A exactly __________ element(s)... Problem 6E: Yes or No? If No, give a reason. Let f be a function. (a) Is it possible that f(1) = 5 and f(2) = 5?... Problem 7E: Function Notation Express the rule in function notation. (For example, the rule square, then... Problem 8E: Function Notation Express the rule in function notation. (For example, the rule square, then... Problem 9E: Function Notation Express the rule in function notation. (For example, the rule square, then... Problem 10E: Function Notation Express the rule in function notation. (For example, the rule square, then... Problem 11E: Functions in Words Express the function (or rule) in words. 11. f(x) = 2x + 3 Problem 12E Problem 13E: Functions in Words Express the function (or rule) in words. 13. h(x) = 5(x + 1) Problem 14E: Functions in Words Express the function (or rule) in words. 14. k(x)=x243 Problem 15E: Machine Diagram Draw a machine diagram for the function. 15. f(x)=x1 Problem 16E: Machine Diagram Draw a machine diagram for the function. 16. f(x)=3x2 Problem 17E: Table of Values Complete the table. 17. f(x) = 2(x 1)2 x f(x) 1 0 1 2 3 Problem 18E: Table of Values Complete the table. 18. g(x) = |2x + 3| x g(x) 3 2 0 1 3 Problem 19E: Evaluating Functions Evaluate the function at the indicated values. 19. f(x) = x2 6; f(3), f(3),... Problem 20E Problem 21E Problem 22E Problem 23E Problem 24E Problem 25E Problem 26E: Evaluating Functions Evaluate the function at the indicated values. 26. g(t)=t+2t2; g(2), g(2),... Problem 27E Problem 28E: Evaluating Functions Evaluate the function at the indicated values. 28. k(x) = 2x3 3x2; k(0), k(3),... Problem 29E: Evaluating Functions Evaluate the function at the indicated values. 29. f(x) = 2 |x 1|; f(2), f(0),... Problem 30E Problem 31E: Piecewise Defined Functions Evaluate the piecewise defined function at the indicated values. 31.... Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E Problem 38E Problem 39E Problem 40E: Net Change Find the net change in the value of the function between the given inputs. 40. f(x) = 4 ... Problem 41E Problem 42E: Net Change Find the net change in the value of the function between the given inputs. 42. h(t) = t2... Problem 43E: Difference Quotient Find f(a), f(a + h), and the difference quotient, f(a+h)f(a)h, where h 0. 43.... Problem 44E: Difference Quotient Find f(a), f(a + h), and the difference quotient, f(a+h)f(a)h, where h 0. 44.... Problem 45E Problem 46E Problem 47E Problem 48E: Difference Quotient Find f(a), f(a + h), and the difference quotient, f(a+h)f(a)h, where h 0. 48.... Problem 49E: Difference Quotient Find f(a), f(a + h), and the difference quotient, f(a+h)f(a)h, where h 0. 49.... Problem 50E Problem 51E: Domain and Range Find the domain and range of the function. 51. f(x) = 3x Problem 52E Problem 53E: Domain and Range Find the domain and range of the function. 53. f(x) = 3x, 2 x 6 Problem 54E: Domain and Range Find the domain and range of the function. 54. f(x) = 5x2 + 4, 0 x 2 Problem 55E: Domain Find the domain of the function. 55. f(x)=1x3 Problem 56E Problem 57E: Domain Find the domain of the function. 57. f(x)=x+2x21 Problem 58E Problem 59E Problem 60E Problem 61E: Domain Find the domain of the function. 61. f(t)=t13 Problem 62E Problem 63E: Domain Find the domain of the function. 63. f(x)=12x Problem 64E Problem 65E Problem 66E Problem 67E: Domain Find the domain of the function. 67. g(x)=x26x4 Problem 68E Problem 69E Problem 70E Problem 71E: Domain Find the domain of the function. 71. f(x)=(x+1)22x1 Problem 72E Problem 73E: Four Ways to Represent a Function A verbal description of a function is given. Find (a) algebraic,... Problem 74E Problem 75E Problem 76E Problem 77E Problem 78E Problem 79E: Torricellis Law A tank holds 50 gal of water, which drains from a leak at the bottom, causing the... Problem 80E Problem 81E: Relativity According to the Theory of Relativity, the length L of an object is a function of its... Problem 82E Problem 83E: Blood Flow As blood moves through a vein or an artery, its velocity v is greatest along the central... Problem 84E: How Far Can You See? Because of the curvature of the earth, the maximum distance D that you can see... Problem 85E: Income Tax In a certain country, income tax T is assessed according to the following function of... Problem 86E: Internet Purchases An Internet bookstore charges 15 shipping for orders under 100 but provides free... Problem 87E: Cost of a Hotel Stay A hotel chain charges 75 each night for the first two nights and 50 for each... Problem 88E: Speeding Tickets In a certain state the maximum speed permitted on freeways is 65 mi/h, and the... Problem 89E: Height of Grass A home owner mows the lawn every Wednesday afternoon. Sketch a rough graph of the... Problem 90E Problem 91E Problem 92E Problem 93E Problem 94E Problem 95E: DISCUSS: Piecewise Defined Functions In Exercises 8588 we worked with real-world situations modeled... format_list_bulleted