MATH College Algebra Review for Test 1

Transcription

1 MATH 34 - College Algebra Review for Test Section.2. For the relation {(,4), (,2), (5, )}, (a) what is the domain and (b) what is the range? 2. (a) For the table of data shown in the table at the right, epress the data as a set of ordered pairs. (b) Give the domain. (c) Give the range Find the eact distance between the points (4, 5) and ( 2, ). 4. Find the midpoint of the line segment connecting the points (4, 5) and ( 2, ). 5. Give the standard form of the equation of the circle shown at the right. 6. Give (a) the center and (b) the radius of the circle whose equation is. 7. Give the standard form of the equation of the circle that has its center at (4, 3) with the point (,9) on the circle. 8. Give the standard form of the equation of the circle that has ends of a diameter at ( 3,4) and (7, 6). Section.3 9. (a) Is the set of ordered pairs {(,3),(4,4), (3,)} a function? Eplain how ou know. (b) Is the relation whose graph is shown at the right a function? Eplain how ou know.

2 MATH 34 - College Algebra - Review for Test (Thomason) - p. 2 of 9 (c) Is the relation given b the following table a function? Eplain how ou know. X Y Determine the domain of each of the following functions. (a) (b) (c). For, determine (a), (b), and (c). 2. (a) True or False: The graph of is a vertical line that passes through 3 on the -ais. (b) True or False: The slope of the line is undefined. 3. The graph of f is shown at the right. (a) What is the range of f? (b) Determine. (c) Determine the value(s) of for which 4. If, identif a point that is on the graph of f. Section.4 5. The graph shown at the right shows the price of ards of carpeting. (a) Find the slope of the graph. (b) Interpret the slope as a rate of change Carpet (square ards) 6. Epress the following in interval notation: 7. Epress the following in interval notation: ] ( For, compute the average rate of change of f from to.

3 9. Use the graph of f at the right to determine the interval(s) in which (a) f is increasing and (b) f is decreasing. Give our answers in interval notation. MATH 34 - College Algebra - Review for Test (Thomason) - p. 3 of 9 Section Let and. Determine each of the following. (a) (b) (c) (d) (e) (f) (g) (h) 2. The graphs of and are shown at the right. Use the graphs to evaluate each of the following. (a) (b) (c) (d) (e) (f) (g) = f() = g() 22. Ra recorded a CD of a song he wrote and performs. It cost him $,500 to have the song recorded and it cost him $2.00 for each CD he had duplicated. He sold the CD s for $4.00 each. (a) What was Ra s total cost function for recording the CD and having copies made? (b) What was Ra s revenue function for the sale of copies of the CD? (c) What was Ra s profit function for the sale of copies of the CD? (Reminder: Profit = Revenue Cost) (d) If Ra had,000 copies of the CD made and sold them all, what was his profit? Section The table at the right is a complete representation of the function f (a) Is f a one-to-one function? Eplain how ou determined our answer. (b) Does f have an inverse function? (c) Evaluate, if possible.

4 MATH 34 - College Algebra - Review for Test (Thomason) - p. 4 of If, find the smbolic representation (the formula) for. 25. Determine the formula for the inverse function of. 26. The graph of is shown on the coordinate sstem at the right. (a) Is a one-to-one function? Eplain how ou determined our answer. (b) On the same coordinate sstem, sketch the graph of. (c) What is the relationship between the graphs of and? ( 4, ) (4,3) 27. For the function shown in Problem 26, determine (a) and (b). Section (a) Is the data in the table at the right linear? (b) If so, determine the slope-intercept form of the equation of the line passing through the data points? 29. Write a formula for the linear function f show in the graph at the right For, (a) give the slope, (b) give the -intercept, (c) give the - intercept, and (d) draw the graph. 3. For, (a) give the slope, (b) give the -intercept, (c) give the -intercept, and (d) draw the graph. 32. For, (a) give the slope, (b) give the -intercept, (c) give the -intercept, and (d) draw the graph.

5 MATH 34 - College Algebra - Review for Test (Thomason) - p. 5 of For, (a) give the slope, (b) give the -intercept, (c) give the -intercept, and (d) draw the graph. 34. A person is riding a biccle along a straight highwa. The graph at the right shows the rider s distance in miles from a First Aid Station after hours. (a) Find the slope-intercept form of the equation of the line. (b) How fast is the bicclist traveling? (c) How far from the First Aid Station was the bicclist initiall? (d) How far from the First Aid Station was the bicclist after 2 hours? 35. Determine the slope-intercept form of the equation of the line that is perpendicular to and that passes through the point (6, ) (,3) (4,3) Determine the slope-intercept form of the equation of the line that is parallel to and that passes through the point (2, 5). 37. In 2005, the number of homes in the U.S. with flat screen televisions was 7.5 million. Since then, the number of homes in the U.S. with flat screen televisions has been increasing at a constant rate of 8.2 million homes per ear. Let t represent the number of ears since 2005 and write a formula for the linear function N that models this situation. 38. In 2000 there were 7.6 million automobiles produced in the United States and in 2004 there were 6.4 million. The formula models these data eactl, where corresponds to 2000, to 200, and so on. Use to estimate the number of automobiles manufactured in the U. S. in In 998 the value of a house was $50,000 and in 2006 the value of the house was $82,000. Find a linear function V that approimates the value of the house in ear. Section Solve the equation: 4. Solve the equation: 42. Solve for b: 43. Jell Beans sell for $2 a pound and Gumm Bears sell for $3 a pound. How man pounds of each kind of cand must be used to produce a 0 pound miture worth a total of $27.50? 44. Suppose Joe, working alone, can rake a certain lawn in 4 hours and that John, working alone, can rake the same lawn in 8 hours. How long would it take Joe and John working together to rake the same lawn?

6 MATH 34 - College Algebra - Review for Test (Thomason) - p. 6 of A rectangular window has a length that is 8 inches more than its width. The perimeter of the window is 00 inches. Find the length and width of the window. 46. A car went 30 miles in 5 hours, traveling part of the time at 55 miles per hour and part of the time at 65 miles per hour. For what length of time did the car travel at each speed? Section Solve for and give the solution in interval notation: 48. Solve for and give the solution in interval notation: 49. Solve and give our solution in interval notation: 50. The total cost of producing copies of a CD is given b. For what number of CDs will the total cost be between $3,75 and $3,900? Section In 2007 about 5.8% of U.S. homes had broadband Internet access. This percentage increased b 2. percentage points per ear for the net 5 ears. (a) Write a formula for the linear function that models this situation. (b) What is the input variable and what does the input variable represent? (c) What is the domain? (Assume the domain is an interval of the real numbers.) (d) What percentage of U.S. homes had broadband in 200? 52. A 500-gallon storage tank is initiall full of gasoline and is being emptied at a rate of 5 gallons per minute. (a) Write a function G that gives the number of gallons of gasoline in the tank after t minutes. (b) How much gasoline remains in the tank after 20 minutes? 53. For the piecewise function f is defined b, determine (a) and (b). (c) Graph f. Section Graph. 55. Solve: 56. Solve: 57. Solve: 58. Solve and give the solution in interval notation: 59. Solve and give the solution in interval notation: Answers. (a) { 3,,5} (b) { 6,2,4} 2. (a) {(4,5),(,2),(0,),(3,2)} (b) {,0,3,4} (c) {,2,5}

7 MATH 34 - College Algebra - Review for Test (Thomason) - p. 7 of (a) (b) (a) Yes, because no first number in the ordered pairs is repeated as a first number. (b) No, because the graph fails the Vertical Line Test. (c) No, because 3 is repeated as a first number in the ordered pairs. 0. (a) (b) (c) (d). (a) 4 (b) (c) 2. (a) F (b) T 3. (a) (b) 3 (c) 3,, 3 4. (5, 2) 5. (a) 7 (b) Carpet cost $7 per sq d (a) (b) 20. (a) (b) (c) (d) (e) (f) (g) 8 (h) 2. (a) (b) 0 (c) undefined (d) 4 (e) 3 (f) 0 (g) (a) (b) (c) (d) $ (a) Yes, because no value is repeated as an value and no value is repeated as a value. (b) Yes. (c) (a) It is a function because it passes the Vertical Line Test and it is a one-to-one function because it passes the Horizontal Line Test. (b) (c) The graphs of and are smmetric to each other about the line. 27. (a) (b)

8 MATH 34 - College Algebra - Review for Test (Thomason) - p. 8 of (a) Yes 30. (a) (b) (4,0) (c) (0,6) 3. (a) (b) (c) (b) (a) 0 (b) none (c) 33. (a) undefined (b) (c) none 34. (a) (b) 6 mph (c) 7 mi (d) 9 mi million lb of Jell Beans, 7.5 lb of Gumm Bears Length: 29 in., Width: 2 in hr at 55 mph, 2.6 hr at 65 mph

9 MATH 34 - College Algebra - Review for Test (Thomason) - p. 9 of Between 35 and 280 CDs. 5. (a) (b) The input variable is t and it represents the number of ears since (c) (d) 22.% 52. (a) (b) 200 gallons 53. (a) 4 (b) 0 (c) No solution