7. Solve the following compound inequality. Write the solution in interval notation.

Transcription

1 1. Write an inequality that describes the graph Use words to describe the line graph. 4. Create a line graph of the inequality. x > 4 4. Write an inequality that describes the graph Write an inequality that describes the graph Use words to describe the line graph Solve the following compound inequality. Write the solution in interval notation. 10x< 10 and x+ 7 > 6 8. Solve the following compound inequality. Write the solution in interval notation. x or 10x Solve the following compound inequality. Write the solution in interval notation. x> 16 and x+ > 10 Chapter Page 1

2 10. Wages The sales agent for a jewelry company is offered a flat monthly salary of $491 or a salary of $14 plus 11% commission on the selling price of each item sold by the agent. If the agent chooses the $491, what dollar amount does the agent expect to sell in 1 month? 11. Comparing Services A computer bulletin board service charges a flat fee of $1 per month or a fee of $4 per month plus $0.15 for each minute the service is used. How many minutes must a person use this service to exceed $1? 1. Transportation A shuttle service taking skiers to a ski resort charges $9.00 per person each way. Four skiers are debating whether to take the shuttle bus or rent a car for $40.00 plus $0.0 per mile. Assuming that the skiers will share the cost of the car and that they want the least expensive method of transport, find how far away the ski area is if they choose the shuttle service. 1. Does the diagram below represent a function? Chapter Page

3 14. Does the diagram below represent a function? 15. State whether the following relation is a function. {(,4),(7,5),(8,7),(, 1),(7, 4)} 16. State whether the following relation is a function. {( 7,6),( 5,6),(,6),(0,6),(,6)} 17. Find the domain and range of the following function. {(4,4),(6,6),(,6),(10,10),( 5,10)} 18. Find the range of the function defined by the equation and the given domain. f( x) = 7 x x ; D= {,0,} 19. Given the function f x ( ) 4x =, find f ( ). 0. Given the function st () = 5t, find s ( ). 1. Given the function f( x) = 4x 5x 4, find f ( 4).. Evaluate the transcript cost function f ( x) = 7 + 6( x 1) for the specified input. f ( n+ p) Chapter Page

4 . Evaluate the transcript cost function f ( x) = 8 + ( x 1) for the specified input. f ( s t) 4. Evaluate the parabolic function f ( x) = x + x + for the specified input. f ( s t) 5. Evaluate the parabolic function f ( x) = x + x + for the specified input. f ( u + v) 6. Find the x- and y-intercepts of the line x+ 5y = Find the x- and y-intercepts of the line y = x Find the x- and y-intercepts and then graph: x y = 0 9. Use f ( 0) to help you find the y-intercept point of the equation. 8 f ( x) = x Use f ( x ) = 0 to help you find the x-intercept point of the equation. 4 f ( x) = x Find the slope of the line containing the given points. P(,8), P(5,14) 1. Find the slope of the line containing the given points. P(1, ), P(, 1) 1 Chapter Page 4

5 . Find the slope of the line containing the given points. P(, ), P(0,0) 1 4. Point (, 10), m =. 5. Point (1, 1), m = Point (7, 6), m = Point (, 7), slope is undefined. 8. Find the equation of the line that contains the points P1(, 8) and P(7, 8). 9. Find the equation of the line that contains the points P1( 8, ) and P( 8, ). 40. P1(5, 1), P(10, ) 41. P1( 1, 0), P(1, 4) 4. P1(0, 0), P( 5, ) 4. P1(0, 1), P ( 5,) 44. A Boeing 747 jet takes off from Boston's Logan Airport, which is at sea level, and climbs to a cruising altitude of,000 ft at a constant rate of 1400 ft/min. a. Write a linear equation for the height of the plane in terms of the time after takeoff. b. Use your equation to find the height of the plane 1 min after takeoff. Chapter Page 5

6 45. A building contractor estimates that the cost to build a home is $4,000 plus $90 for each square foot of floor space in the house. a. Determine a linear function that will give the cost of building a house that contains a given number of square feet of floor space. b. Use this model to determine the cost to build a house that contains 1500 square feet of floor space. 46. A cellular phone company offers several different service plans. One option, for people who plan on using the phone only in emergencies, costs the user $4.65 per month plus $0.6 per minute for each minute the phone is used. a. Write a linear function for the monthly cost of the phone in terms of the number of minutes the phone is used. b. Use your equation to find the cost of using the cellular phone for 15 minutes in 1 month. 47. The gas tank of a certain car contains 1 gal of gas when the driver of the car begins a trip. Each mile driven by the driver decreases the amount of gas in the tank by 0.06 gal. a. Write a linear function for the number of gallons of gas in the tank in terms of the number of miles driven. b. Use your equation to find the number of gallons in the tank after driving 1 mi. Round your answer to the nearest tenth of a gallon. 48. A manufacturer of graphing calculators has determined that 8000 calculators per week will be sold at a price of $105 each. At a price of $85, it is estimated that 14,000 calculators would be sold. a. Determine a linear function that will predict the number of calculators that would be sold at a given price, x. b. Use this model to predict the number of calculators that would be sold each week at a price of $ Graph by using the slope and y-intercept: y = x Write a linear equation for the following facts: y-intercept, slope Chapter Page 6

7 51. Graph by using the slope and y-intercept: y = x 4 5. Write a linear equation for the following facts: y-intercept 5, x-intercept 8 5. Find the equation of the line that passes through the following points: (, 4) and ( 9, 4) 54. Find the equation of the line passing through the given point with the indicated slope. Point (, 1 ), zero slope 55. Find the equation of the line passing through the given point with the indicated slope. Point (, 7), undefined slope 56. Find the equation of the line that passing through the given point with the indicated slope. Origin, zero slope 57. The slope of a line is. What is the slope of any line parallel to this line? Is the system parallel, perpendicular, or neither? y = x x = y+ x The slope of a line is 7. What is the slope of any line perpendicular to this line? 60. Is the system parallel, perpendicular, or neither? y 4 x = 1 ( x ) y = Find the equation of the line fitting the information given. Parallel to x+ 7 y = 6 and passing through the origin Chapter Page 7

8 6. Find the equation of the line containing the point (10, 1) and perpendicular to the line y = 9x Find the equation of the line containing the point (, 11) and perpendicular to the line 10x+ 0 y = Find the equation of the line containing the point (, ) and parallel to the line x+ y = Find the equation of the line fitting the information given. Perpendicular to 5 + 6, 5 x y = and passing through ( ) 66. Is x = 1 a solution of the equation 6x 7 = 14? 67. Solve x = Solve y = Solve x = Solve x + 4 = Solve y 7 = Solve y 9 = Solve x 5 = Solve 9 11 x = Solve x 7 7= 1. Chapter Page 8

9 76. Solve 9a + 7= Solve x 10 7 = Solve 9 x 5 = Solve 1 8 x + 6 = Solve 8 8x + 7 =. Chapter Page 9

10 Answer Key 1. x < 1. x is between and 4, including and < x < 5. x< 5 or x> 6. x is less than 0 or greater than 6 7. ( 1,1) 8. (,1] [ 6, ) $18, > 60 min 1. > 80 mi 1. Yes 14. No 15. Not a function 16. Function 17. D: { 5,, 4, 6, 10}; R: {4, 6, 10} 18. {14,, 8} n+ 6 p+ 1. s t s st + t + s t + 5. u + uv + v + u + v + 6. x-intercept: (15, 0), y-intercept: (0, 6) 7. x-intercept: (, 0), y-intercept: (0, 6) Chapter Page 10

11 8. x-intercept: (0, 0), y-intercept: (0, 0) 9. ( 0, 8) 45 0., y = x 4 5. y = 4 x y = x x = 8. y = 8 9. x = y = x+ 41. y = x+ 4. y = x 5 4. y = x (a) y = 1400 x, 0 x ; (b) 9,400 ft (a) y = 90x+ 4,000 ; (b) $169, (a) y = 0.6x+ 4.65; (b) $ (a) y = 0.06x+ 1, 0 x ; (b) 7. gal 48. (a) y = 00 x+ 9500; (b) 0,000 calculators Chapter Page 11

12 y = x y = x y = y = x = 56. y = parallel neither 61. y = x 7 Chapter Page 1

13 y = x y = x y = x y = x No 67. Both A and B 68. Both B and C 69. No solution 70. Both A and B 71. Both B and C No solution 74. Both A and B 75. Both B and C 76. Both A and C 77. Both A and B 78. Both A and B 79. Both B and C 80. Both A and C Chapter Page 1