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All Textbook Solutions for Precalculus Enhanced with Graphing Utilities

In Problems 31-42, determine whether the equation defines y as a function of x. y= x 3 In Problems 31-42, determine whether the equation defines y as a function of x. y= x 3 In Problems 31-42, determine whether the equation defines y as a function of x . y=| x |In Problems 31-42, determine whether the equation defines y as a function of x . y 2 =4 x 2 In Problems 31-42, determine whether the equation defines y as a function of x . y= 12x In Problems 31-42, determine whether the equation defines y as a function of x . x= y 2 In Problems 31-42, determine whether the equation defines y as a function of x . x+ y 2 =1 In Problems 31-42, determine whether the equation defines y as a function of x . y= x 3 In Problems 31-42, determine whether the equation defines y as a function of x . y= 3x1 x+2 In Problems 31-42, determine whether the equation defines y as a function of x . 2 x 2 +3 y 2 =1 In Problems 31-42, determine whether the equation defines y as a function of x . x 2 4 y 2 =1 In problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )=3 x 2 +2x4 In problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )=2 x 2 +x1 41AYU In problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )= x 2 1 x+4 In problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )=| x |+4 In problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )= x 2 + x In problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )= 2x+1 3x5 46AYU In Problems 51-66, find the domain of each function. f( x )=5x+4 In Problems 51-66, find the domain of each function. f( x )= x 2 +2 In Problems 51-66, find the domain of each function. f( x )= x x 2 +1 50AYU In Problems 51-66, find the domain of each function. g( x )= x x 2 -16 In Problems 51-66, find the domain of each function. h( x )= 2x x 2 -4 In Problems 51-66, find the domain of each function. F( x )= x-2 x 3 +x In Problems 51-66, find the domain of each function. G( x )= x+4 x 3 -4x In Problems 51-66, find the domain of each function. h( x )= 3x-12 In Problems 51-66, find the domain of each function. G( x )= 1-x In Problems 51-66, find the domain of each function. p( x )= 2 x-1 58AYU 59AYU 60AYU 61AYU 62AYU In problems 67-76, for the given functions f and g , find the following. For parts (a)-(d), also find the domain. a. ( f+g )( x ) b. ( f-g )( x ) c. ( fg )( x ) d. ( f g )( x ) e. ( f+g )( 4 ) f. ( f-g )( 3 ) g. ( fg )( 2 ) h. ( f g )( 1 ) f( x )=3x+4 ; g( x )=2x-3 In problems 67-76, for the given functions f and g , find the following. For parts (a)-(d), also find the domain. a. ( f+g )( x ) b. ( f-g )( x ) c. ( fg )( x ) d. ( f g )( x ) e. ( f+g )( 4 ) f. ( f-g )( 3 ) g. ( fg )( 2 ) h. ( f g )( 1 ) f( x )=2x+1 ; g( x )=3x-2 65AYU In problems 67-76, for the given functions f and g , find the following. For parts (a)-(d), also find the domain. a. ( f+g )( x ) b. ( f-g )( x ) c. ( fg )( x ) d. ( f g )( x ) e. ( f+g )( 4 ) f. ( f-g )( 3 ) g. ( fg )( 2 ) h. ( f g )( 1 ) f( x )=2 x 2 +3 ; g( x )=4 x 3 +1 In problems 67-76, for the given functions f and g , find the following. For parts (a)-(d), also find the domain. a. ( f+g )( x ) b. ( f-g )( x ) c. ( fg )( x ) d. ( f g )( x ) e. ( f+g )( 4 ) f. ( f-g )( 3 ) g. ( fg )( 2 ) h. ( f g )( 1 ) f( x )= x ; g( x )=3x-5 68AYU In problems 67-76, for the given functions f and g , find the following. For parts (a)-(d), also find the domain. a. ( f+g )( x ) b. ( f-g )( x ) c. ( fg )( x ) d. ( f g )( x ) e. ( f+g )( 4 ) f. ( f-g )( 3 ) g. ( fg )( 2 ) h. ( f g )( 1 ) f( x )=1+ 1 x ; g( x )= 1 x 70AYU In problems 67-76, for the given functions f and g , find the following. For parts (a)-(d), also find the domain. a. ( f+g )( x ) b. ( f-g )( x ) c. ( fg )( x ) d. ( f g )( x ) e. ( f+g )( 4 ) f. ( f-g )( 3 ) g. ( fg )( 2 ) h. ( f g )( 1 ) f( x )= 2x+3 3x-2 ; g( x )= 4x 3x-2 In problems 67-76, for the given functions f and g , find the following. For parts (a)-(d), also find the domain. a. ( f+g )( x ) b. ( f-g )( x ) c. ( fg )( x ) d. ( f g )( x ) e. ( f+g )( 4 ) f. ( f-g )( 3 ) g. ( fg )( 2 ) h. ( f g )( 1 ) f( x )= x+1 ; g( x )= 2 x Given f( x )=3x+1 and ( f+g )( x )=6- 1 2 x , find the function g .Given f( x )= 1 x and ( f g )( x )= x+1 x 2 -x , find the function g .In Problems 79-90, find the difference quotient of f ; that is, find f( x+h )-f( x ) h , h0 , for each function. Be sure to simplify. f( x )=4x+3 76AYU In Problems 79-90, find the difference quotient of f ; that is, find f( x+h )-f( x ) h , h0 , for each function. Be sure to simplify. f( x )= x 2 -x+4 In Problems 79-90, find the difference quotient of f ; that is, find f( x+h )-f( x ) h , h0 , for each function. Be sure to simplify. f( x )=3 x 2 -2x+6 In Problems 79-90, find the difference quotient of f ; that is, find f( x+h )-f( x ) h , h0 , for each function. Be sure to simplify. f( x )= 1 x 2 In Problems 79-90, find the difference quotient of f ; that is, find f( x+h )-f( x ) h , h0 , for each function. Be sure to simplify. f( x )= 1 x+3 81AYU In Problems 79-90, find the difference quotient of f ; that is, find f( x+h )-f( x ) h , h0 , for each function. Be sure to simplify. f( x )= x+1 Given f( x )= x 2 -2x+3 , find the value(s) for x such that f( x )=11 .84AYU 85AYU 86AYU 87AYU 88AYU 89AYU 90AYU Constructing Functions Express the gross salary G of a person who earns 14 per hour as a function of the number x of hours worked.92AYU 93AYU 94AYU Effect of Gravity on Earth If a rock falls from a height of 20 meters on Earth, the height H (in meters) after x seconds is approximately H( x )=204.9 x 2 a. What is the height of the rock when x=1 second? x=1.1 seconds? x=1.2 seconds? x=1.3 seconds? b. When is the height of the rock 15 meters? When is it 10 meters? When is it 5 meters? c. When does the rock strike the ground?96AYU Cost of Transatlantic Travel A Boeing 747 crosses the Atlantic Ocean (3000 miles) with an airspeed of 500 miles per hour. The cost C (in dollars) per passenger is given by C( x )=100+ x 10 + 36,000 x where x is the ground speed (airspeed wind). a. What is the cost per passenger for quiescent (no wind) conditions? b. What is the cost per passenger with a head wind of 50 miles per hour? c. What is the cost per passenger with a tail wind of 100 miles per hour? d. What is the cost per passenger with a head wind of 100 miles per hour?98AYU 99AYU 100AYU 101AYU 102AYU Profit Function Suppose that the revenue R , in dollars, from selling x cell phones, in hundreds, is R( x )=1.2 x 2 +220x . The cost C , in dollars, of selling x cell phones, in hundreds, is C( x )=0.05 x 3 2 x 2 +65x+500 . a. Find the profit function, P( x )=R( x )C( x ) . b. Find the profit if x=15 hundred cell phones are sold. c. Interpret P( 15 ) .104AYU 105AYU Are the functions f( x )=x1 and g( x )= x 2 1 x+1 the same? Explain.Investigate when, historically, the use of the function notation y=f( x ) first appeared.108AYU The intercepts of the equation x 2 +4 y 2 =16 are _______. (pp. 18-19)True or False The point ( 2,6 ) is on the graph of the equation x=2y2 . (pp. 7-11)3. A set of points in the xy -plane is the graph of a function if and only if every _______ line intersects the graph in at most one point.4. If the point ( 5,3 ) is a point on the graph of f , then f( )= _________.5. Find a so that the point ( 1,2 ) is on the graph of f( x )=a x 2 +4 .True or False Every graph represents a function.True or False The graph of a function y=f( x ) always crosses the y-axis .True or False The y-intercept of the graph of the function y=f( x ) , whose domain is all real numbers, is f( 0 ) .Use the given graph the function f to answer parts (a)-(n). (a) Find f( 0 ) and f( 6 ) . (b) Find f( 6 ) and f( 11 ) . (c) Is f( 3 ) positive or negative? (d) Is f( 4 ) positive or negative? (e) For what values of x is f( x )=0 ? (f) For what values of x is f( x )0 ? (g) What is the domain of f ? (h) What is the range of f ? (i) What are the x-intercepts ? (j) What is the y-intercept ? (k) How often does the line y= 1 2 intersect the graph? (l) How often does the line x=5 intersect the graph? (m) For what values of x does f( x )=3 ? (n) For what values of x does f( x )=2 ?Use the given graph the function f to answer parts (a)-(n). (a) Find f( 0 ) and f( 6 ) . (b) Find f( 2 ) and f( 2 ) . (c) Is f( 3 ) positive or negative? (d) Is f( 1 ) positive or negative? (e) For what values of x is f( x )=0 ? (f) For what values of x is f( x )0 ? (g) What is the domain of f ? (h) What is the range of f ? (i) What are the x-intercepts ? (j) What is the y-intercept ? (k) How often does the line y=1 intersect the graph? (l) How often does the line x=1 intersect the graph? (m) For what values of x does f( x )=3 ? (n) For what values of f( x )=2 ?In Problems 13-24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis , the y-axis , or the origin In Problems 13-24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis , the y-axis , or the origin In Problems 13-24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis , the y-axis , or the origin In Problems 13-24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis , the y-axis , or the origin In Problems 13-24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis , the y-axis , or the origin In Problems 13-24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis , the y-axis , or the origin In Problems 13-24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis , the y-axis , or the origin In Problems 13-24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis , the y-axis , or the origin In Problems 13-24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis , the y-axis , or the origin In Problems 13-24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis , the y-axis , or the origin In Problems 13-24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis , the y-axis , or the origin In Problems 13-24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis , the y-axis , or the origin In Problems 25-30, answer the questions about the given function. f( x )=2 x 2 x1 (a) Is the point ( 1,2 ) on the graph of f ? (b) If x=2 . what is f( x ) ? What point is on the graph of f ? (c) If f( x )=1 , what is x ? What point(s) are on the graph of f ? (d) What is the domain of f ? (e) List the x-intercepts ., if any, of the graph of f . (f) List the y-intercepts , if there is one, of the graph of f .In Problems 25-30, answer the questions about the given function. f( x )=-3 x 2 +5x (a) Is the point ( 1,2 ) on the graph of f ? (b) If x=2 . what is f( x ) ? What point is on the graph of f ? (c) If f( x )=2 , what is x ? What point(s) are on the graph of f ? (d) What is the domain of f ? (e) List the x-intercepts , if any, of the graph of f . (f) List the y-intercepts , if there is one, of the graph of f .25AYU In Problems 25-30, answer the questions about the given function. f( x )= x 2 +2 x+4 (a) Is the point ( 1, 3 5 ) on the graph of f ? (b) If x=0 . what is f( x ) ? What point is on the graph of f ? (c) If f( x )= 1 2 , what is x ? What point(s) are on the graph of f ? (d) What is the domain of f ? (e) List the x-intercepts , if any, of the graph of f . (f) List the y-intercepts , if there is one, of the graph of f .27AYU In Problems 25-30, answer the questions about the given function. f( x )= 2x x2 (a) Is the point ( 1 2 , 2 3 ) on the graph of f ? (b) If x=4 . what is f( x ) ? What point is on the graph of f ? (c) If f( x )=1 , what is x ? What point(s) are on the graph of f ? (d) What is the domain of f ? (e) List the x-intercepts ., if any, of the graph of f . (f) List the y-intercepts , if there is one, of the graph of f .29AYU 30AYU 33AYU 34AYU 35AYU 36AYU 37AYU 38AYU 39AYU 40AYU 41AYU 42AYU 43AYU 44AYU 45AYU 46AYU 47AYU 48AYU â€˜Are You Prepared?' Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 1. The interval ( 2,5 ) can be written as the inequality ______. (pp. A76-A77)â€˜Are You Prepared?' Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 2. The slope of the line containing the points ( 2,3 ) and ( 3,8 ) is ______. (pp. 30-32)â€˜Are You Prepared?' Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 3. Test the equation y=5 x 2 1 for symmetry with respect to the x-axis , the y-axis , and the origin. (pp. 19-21)â€˜Are You Prepared?' Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 4. Write the point-slope form of the line with slope 5 containing the point ( 3,2 ) . (p. 33)â€˜Are You Prepared?' Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 5. The intercepts of the equation y= x 2 9 are ______. (pp. 18-19)6. A function f is _____ on an interval I if, for any choice of x 1 , and x 2 in I , with x 1 x 2 we have f( x 1 )f( x 2 ) .7. A(n) ______ function f is one for which f( x )=f( x ) for every x in the domain of f ; a(n) ______ function f is one for which f( x )=f( x ) for every x in the domain of f .8. True or False A function f is decreasing on an interval I if, for any choice of x 1 and x 2 in I , with x 1 x 2 , we have f( x 1 )f( x 2 ) .9. True or False A function f has a local maximum at c if there is an open interval I containing c such that for all x in I , f( x )f( c )10. True or False Even functions have graphs that are symmetric with respect to the origin.In Problems 13-24, use the graph of the function f given. 13. Is f increasing on the interval [ 8,2 ] ?In Problems 13-24, use the graph of the function f given. 14. Is f decreasing on the interval [ 8,4 ] ?In Problems 13-24, use the graph of the function f given. 15. Is f increasing on the interval [ 2,6 ] ?In Problems 13-24, use the graph of the function f given. 16. Is f decreasing on the interval [ 2,5 ] ?In Problems 13-24, use the graph of the function f given. 17. List the interval(s) on which f increasing.In Problems 13-24, use the graph of the function f given. 18. List the interval(s) on which f decreasing.In Problems 13-24, use the graph of the function f given. 19. Is there a local maximum at 2? If yes, what is it?In Problems 13-24, use the graph of the function f given. 20. Is there a local maximum at 5? If yes, what is it?In Problems 13-24, use the graph of the function f given. 21. List the number(s) at which f has a local maximum. What are the local maximum values?In Problems 13-24, use the graph of the function f given. 22. List the number(s) at which f has a local minimum. What are the local minimum values?In Problems 25-32, the graph of a function is given. Use the graph to find: a. The intercepts, if any b. The domain and range c. The intervals on which the function is increasing, decreasing, or constant d. Whether the function is even, odd, or neither 25.In Problems 25-32, the graph of a function is given. Use the graph to find: a. The intercepts, if any b. The domain and range c. The intervals on which the function is increasing, decreasing, or constant d. Whether the function is even, odd, or neither 26.In Problems 25-32, the graph of a function is given. Use the graph to find: a. The intercepts, if any b. The domain and range c. The intervals on which the function is increasing, decreasing, or constant d. Whether the function is even, odd, or neither 27.In Problems 25-32, the graph of a function is given. Use the graph to find: a. The intercepts, if any b. The domain and range c. The intervals on which the function is increasing, decreasing, or constant d. Whether the function is even, odd, or neither 28.In Problems 25-32, the graph of a function is given. Use the graph to find: a. The intercepts, if any b. The domain and range c. The intervals on which the function is increasing, decreasing, or constant d. Whether the function is even, odd, or neither 29.In Problems 25-32, the graph of a function is given. Use the graph to find: a. The intercepts, if any b. The domain and range c. The intervals on which the function is increasing, decreasing, or constant d. Whether the function is even, odd, or neither 30.In Problems 25-32, the graph of a function is given. Use the graph to find: a. The intercepts, if any b. The domain and range c. The intervals on which the function is increasing, decreasing, or constant d. Whether the function is even, odd, or neither 31.In Problems 25-32, the graph of a function is given. Use the graph to find: a. The intercepts, if any b. The domain and range c. The intervals on which the function is increasing, decreasing, or constant d. Whether the function is even, odd, or neither 32.In Problems 33-36, the graph of a function f is given. Use the graph to find: a. The numbers, if any, at which f has a local maximum. What are the local maximum values? b. The numbers, if any, at which f has a local minimum. What are the local minimum values? 33.In Problems 33-36, the graph of a function f is given. Use the graph to find: a. The numbers, if any, at which f has a local maximum. What are the local maximum values? b. The numbers, if any, at which f has a local minimum. What are the local minimum values? 34.In Problems 33-36, the graph of a function f is given. Use the graph to find: a. The numbers, if any, at which f has a local maximum. What are the local maximum values? b. The numbers, if any, at which f has a local minimum. What are the local minimum values? 35.In Problems 33-36, the graph of a function f is given. Use the graph to find: a. The numbers, if any, at which f has a local maximum. What are the local maximum values? b. The numbers, if any, at which f has a local minimum. What are the local minimum values? 36.In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 37. f( x )=4 x 3 In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 38. f( x )=2 x 4 x 2 In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 39. g( x )=3 x 2 5 In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 40. h( x )=3 x 3 +5 In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 41. F( x )= x 3 In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 42. G( x )= x In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 43. f( x )=x+| x |In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 44. f( x )= 2 x 2 +1 3 In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 45. g( x )= 1 x 2 In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 46. h( x )= x x 2 1 In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 47. h( x )= x 3 3 x 2 9 In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 48. F( x )= 2x | x |In Problem 49-56, for each graph of a function y=f( x ) , find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values. 49.In Problem 49-56, for each graph of a function y=f( x ) , find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values. 50.In Problem 49-56, for each graph of a function y=f( x ) , find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values. 51.In Problem 49-56, for each graph of a function y=f( x ) , find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values. 52.In Problem 49-56, for each graph of a function y=f( x ) , find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values. 53.In Problems 49-56, for each graph of a function y=f( x ) , find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values. 54.In Problems 49-56, for each graph of a function y=f( x ) , find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values. 55.In Problems 49-56, for each graph of a function y=f( x ) , find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values. 56.In Problems 57-64, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places. 57. f( x )= x 3 3x+2[ 2,2 ]In Problems 57-64, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places. 58. f( x )= x 3 3 x 2 +5[ 1,3 ]In Problems 57-64, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places. 59. f( x )= x 5 x 3 [ 2,2 ]In Problems 57-64, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places. 60. f( x )= x 4 x 2 [ 2,2 ]In Problems 57-64, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places. 61. f( x )=0.2 x 3 0.6 x 2 +4x6[ 6,4 ]In Problems 57-64, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places. 62. f( x )=0.4 x 3 +0.6 x 2 +3x2[ 4,5 ]In Problems 57-64, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places. 63. f( x )=0.25 x 4 +0.3 x 3 0.9 x 2 +3[ 3,2 ]In Problems 57-64, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places. 64. f( x )=0.4 x 4 0.5 x 3 +0.8 x 2 2[ 3,2 ]65. Find the average rate of change of f( x )=2 x 2 +4 (a) From 0 to 2 (b) From 1 to 3 (c) From 1 to 4 (d) By hand, graph f and illustrate the average rate of change found in parts (a), (b), and (c).66. Find the average rate of change of f( x )= x 3 +1 : (a) From 0 to 2 (b) From 1 to 3 (c) From -1 to 1 (d) By hand, graph f and illustrate the average rate of change found in parts (a), (b), and (c).67. Find the average rate of change of g( x )= x 3 2x+1 : (a) From -3 to -2 (b) From -1 to 1 (c) From 1 to 3 68. Find the average rate of change of h( x )= x 2 2x+3 : (a) From -1 to 1 (b) From 0 to 2 (c) From 2 to 5 69. f( x )=5x2 (a) Find the average rate of change from 1 to 3. (a) Find an equation of the secant line containing ( 1,f( 1 ) ) and ( 3,f( 3 ) ) .70. f( x )=4x+1 (a) Find the average rate of change from 2 to 5. (b) Find an equation of the secant line containing ( 2,f( 2 ) ) and ( 5,f( 5 ) ) .71. g( x )= x 2 2 (a) Find the average rate of change from -2 to 1. (b) Find an equation of the secant line containing ( 2,g( 2 ) ) and ( 1,g( 1 ) ) . (c) Using a graphing utility, draw the graph of g and the secant line obtained in part (b) on the same screen.72. g( x )= x 2 +1 (a) Find the average rate of change from -1 to 2. (b) Find an equation of the secant line containing ( 1,g( 1 ) ) and ( 2,g( 2 ) ) . (c) Using a graphing utility, draw the graph of g and the secant line obtained in part (b) on the same screen.73. h( x )= x 2 2x (a) Find the average rate of change from 2 to 4. (b) Find an equation of the secant line containing ( 2,h( 2 ) ) and ( 4,h( 4 ) ) . (c) Using a graphing utility, draw the graph of h and the secant line obtained in part (b) on the same screen.74. h( x )=2 x 2 +x (a) Find the average rate of change from 0 to 3. (b) Find an equation of the secant line containing ( 0,h( 0 ) ) and ( 3,h( 3 ) ) . (c) Using a graphing utility, draw the graph of h and the secant line obtained in part (b) on the same screen.75. g( x )= x 3 27x (a) Determine whether g is even, odd, or neither. (b) There is a local minimum value of 54 at 3. Determine the local maximum value.76. f( x )= x 3 +12x (a) Determine whether f is even, odd, or neither. (b) There is a local maximum value of 16 at 2. Determine the local minimum value.77. F( x )= x 4 +8 x 2 +9 (a) Determine whether F is even, odd, or neither. (b) There is a local maximum value of 25 at x=2 . Determine a second local maximum value. (c) Suppose the area under the graph of F between x=0 and x=3 that is bounded from below by the x-axis axis is 50.4 square units. Using the result from part (a), determine the area under the graph of F between x=3 and x=0 that is bounded from below by the x-axis .78. G( x )= x 4 +32 x 2 +144 (a) Determine whether G is even, odd, or neither. (b) There is a local maximum value of 400 at x=4 . Determine a second local maximum value. (c) Suppose the area under the graph of G between x=0 and x=6 that is bounded from below by the x-axis axis is 1612.8 square units. Using the result from part (a), determine the area under the graph of G between x=6 and x=0 that is bounded from below by the x-axis .75AYU 76AYU 77AYU 78AYU 79AYU 80AYU 81AYU 82AYU 83AYU 84AYU 85AYU 86AYU 87AYU 88AYU 89AYU 90AYU 91AYU 92AYU 93AYU 94AYU 95AYU 96AYU Sketch the graph of y= x . (p. 22)Sketch the graph of y= 1 x . (pp. 22-23)List the intercepts of the equation y= x 3 8 . (pp. 18-19)The function f( x )= x 2 is decreasing on the interval ______.When functions are defined by more than one equation, they are called ______ functions.True or False The cube function is odd and is increasing on the interval ( , ) .True or False The cube root function is odd and is decreasing on the interval ( , ) .True or False The domain and the range of the reciprocal function are the set of all real numbers.In Problems 11-18, match each graph to its function. A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function H. Cube root function In Problems 11-18, match each graph to its function. A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function H. Cube root function In Problems 11-18, match each graph to its function. A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function H. Cube root function In Problems 11-18, match each graph to its function. A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function H. Cube root function In Problems 11-18, match each graph to its function. A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function H. Cube root function In Problems 11-18, match each graph to its function. A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function H. Cube root function In Problems 11-18, match each graph to its function. A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function H. Cube root function In Problems 11-18, match each graph to its function. A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function H. Cube root function In Problems 19-26, sketch the graph of each function. Be sure to label three points on the graph. f( x )=x In Problems 19-26, sketch the graph of each function. Be sure to label three points on the graph. f( x )= x 2 In Problems 19-26, sketch the graph of each function. Be sure to label three points on the graph. f( x )= x 3 In Problems 19-26, sketch the graph of each function. Be sure to label three points on the graph. f( x )= x In Problems 19-26, sketch the graph of each function. Be sure to label three points on the graph. f( x )= 1 x In Problems 19-26, sketch the graph of each function. Be sure to label three points on the graph. f( x )=| x |In Problems 19-26, sketch the graph of each function. Be sure to label three points on the graph. f( x )= x 3 In Problems 19-26, sketch the graph of each function. Be sure to label three points on the graph. f( x )=3 If f( x )={ x 2 ifx0 2ifx=0 2x+1ifx0 find: (a) f( 2 ) (b) f( 0 ) (c) f( 2 )If f( x )={ 3xifx1 0ifx=1 2 x 2 +1ifx1 find: (a) f( 2 ) (b) f( 1 ) (c) f( 0 )If f( x )={ 2x4if1x2 x 3 2if2x3 find: (a) f( 0 ) (b) f( 1 ) (c) f( 2 ) (d) f( 3 )If f( x )={ x 3 if2x1 3x+2if1x4 find: (a) f( 1 ) (b) f( 0 ) (c) f( 1 ) (d) f( 3 )In Problems 31-42: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. f( x )={ 2xifx0 1ifx=0 In Problems 31-42: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. f( x )={ 3xifx0 4ifx=0 In Problems 31-42: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. f( x )={ 2x+3ifx1 3x2ifx1 In Problems 31-42: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. f( x )={ x+3ifx2 2x3ifx2 In Problems 31-42: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. f( x )={ x+3if2x1 5ifx=1 x+2ifx1 In Problems 31-42: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. f( x )={ 2x+5if3x0 3ifx=0 5xifx0 In Problems 31-42: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. f( x )={ 1+xifx0 x 2 ifx0 In Problems 31-42: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. f( x )={ 1 x ifx0 x 3 ifx0 In Problems 31-42: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. f( x )={ | x |if2x0 x 3 ifx0 In Problems 31-42: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. f( x )={ 2xif3x1 x ifx1 In Problems 31-42: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. f( x )=2int( x )In Problems 31-42: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. f( x )=int( 2x )In Problems 43-46, the graph of a piecewise-defined function is given. Write a definition for each function.In Problems 43-46, the graph of a piecewise-defined function is given. Write a definition for each function.In Problems 43-46, the graph of a piecewise-defined function is given. Write a definition for each function.In Problems 43-46, the graph of a piecewise-defined function is given. Write a definition for each function.If f( x )=int( 2x ) , find (a) f( 1.2 ) (b) f( 1.6 ) (c) f( 1.8 )46AYU 47AYU 48AYU 49AYU 50AYU 51AYU 52AYU 53AYU 54AYU 55AYU 56AYU 57AYU 58AYU 59AYU 60AYU 61AYU 62AYU 63AYU 64AYU 65AYU 66AYU 67AYU 68AYU 69AYU 1AYU 2AYU 3AYU 4AYU 5AYU 6AYU In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C. y=| x |+2 D. y=-| x |+2 E. y= ( x-2 ) 2 F. y=- ( x+2 ) 2 G. y=| x-2 | H. y=-| x+2 | I. y=2 x 2 J. y=-2 x 2 K. y=2| x | L. y=-2| x |In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C. y=| x |+2 D. y=-| x |+2 E. y= ( x-2 ) 2 F. y=- ( x+2 ) 2 G. y=| x-2 | H. y=-| x+2 | I. y=2 x 2 J. y=-2 x 2 K. y=2| x | L. y=-2| x |

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