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Linear Functions

Math · Algebra · 87 questions · every one comes with a full explanation.

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  1. 1A rectangle has a length that is 15 times its width. The function y=15ww represents this situation, where y is the area, in square feet, of the rectangle and y>0. Which of the foMedium · Advanced Math
  2. 2The function h is defined by hx=4x+28. The graph of y=hx in the xy-plane has an x-intercept at a,0 and a y-intercept at 0,b, where a and b are constants. What is the value of Medium · Algebra
  3. 3According to a model, the head width, in millimeters, of a worker bumblebee can be estimated by adding 0.6 to four times the body weight of the bee, in grams. According to the modeMedium · Algebra
  4. 4Time (years) Total amount (dollars) 0 604.00 1 606.42 2 608.84 Rosa opened a savings account at a bank. The table shows the exponential relationship between the time t , in yeaMedium · Advanced Math
  5. 5f(x)=39 For the given linear function f , which table gives three values of x and their corresponding values of fx?Medium · Algebra
  6. 6A rectangular volleyball court has an area of 162 square meters. If the length of the court is twice the width, what is the width of the court, in meters?Medium · Advanced Math
  7. 7In the xy-plane, the graph of the linear function f contains the points 0,3 and 7,31. Which equation defines f , where y=fx?Medium · Algebra
  8. 8The function S above models the annual salary, in dollars, of an employee n years after starting a job, where a is a constant. If the employee's salary increases by 4% each year, wMedium · Advanced Math
  9. 9The equation above estimates the global data traffic D, in terabytes, for the year that is t years after 2010. What is the best interpretation of the number 5,640 in this context?Medium · Advanced Math
  10. 10In quadrant 3: The curve rises sharply to touch the x axis at point (negative 5 comma 0). The curve falls gradually to a relative minimum at point (negative 2 comma negative 11). Medium · Advanced Math
  11. 11A model predicts that a certain animal weighed 241 pounds when it was born and that the animal gained 3 pounds per day in its first year of life. This model is defined by an equaMedium · Algebra
  12. 12In quadrant 2 the curve falls sharply to cross the x axis at point (negative 1 comma 0). In quadrant 3 the curve falls sharply to cross the y axis at point (0 comma negative 5.5). Medium · Advanced Math
  13. 13A rectangle has a length of x units and a width of x-15 units. If the rectangle has an area of 76 square units, what is the value of x ?Medium · Advanced Math
  14. 14A scientist initially measures 12,000 bacteria in a growth medium. 4 hours later, the scientist measures 24,000 bacteria. Assuming exponential growth, the formula P=C2rt gives tMedium · Advanced Math
  15. 15The graph of this equation in the xy-plane is a line. What is the best interpretation of the x-intercept in this context?Medium · Algebra
  16. 16gx=x2+55 What is the minimum value of the given function?Medium · Advanced Math
  17. 17The function f is defined by f(x)=7x-84. What is the x-intercept of the graph of y=f(x) in the xy-plane?Medium · Algebra
  18. 18x 10 15 20 25 fx 82 137 192 247 The table shows four values of x and their corresponding values of fx. There is a linear relationship between x and fx that is defined byMedium · Algebra
  19. 19fx=x+6x-4 If the given function f is graphed in the xy-plane, where y=fx, what is the x-coordinate of an x-intercept of the graph?Medium · Advanced Math
  20. 20The graph of the function f , where y=f(x), gives the total cost y , in dollars, for a certain video game system and x games. What is the best interpretation of the slope of the gMedium · Algebra
  21. 21Immanuel purchased a certain rare coin on January 1. The function f(x)=651.03x, where 0≤x≤10, gives the predicted value, in dollars, of the rare coin x years after Immanuel purchaMedium · Advanced Math
  22. 22From 2005 through 2014, the number of music CDs sold in the United States declined each year by approximately 15% of the number sold the preceding year. In 2005, approximately 600 Medium · Advanced Math
  23. 23Moving from left to right: The curve is in quadrant 1. From point (0 comma 9), the curve trends down sharply. From point (5 comma 1), the curve trends down gradually. The graph gMedium · Advanced Math
  24. 24Caleb used juice to make popsicles. The function fx=-5x+30 approximates the volume, in fluid ounces, of juice Caleb had remaining after making x popsicles. Which statement is the Medium · Algebra
  25. 25f(x)=(x+6)(x+5)(x-4) The function f is given. Which table of values represents y=f(x)-3?Medium · Advanced Math
  26. 26In the xy-plane, the graph of the linear function f contains the points 0,2 and 8,34. Which equation defines f , where y=fx?Medium · Algebra
  27. 27The product of two positive integers is 546 . If the first integer is 11 greater than twice the second integer, what is the smaller of the two integers?Medium · Advanced Math
  28. 28In the xy-plane, the y-coordinate of the y-intercept of the graph of the function f is c. Which of the following must be equal to c ?Medium · Advanced Math
  29. 29y = 0.25 x 2 - 7.5 x + 90.25 The equation gives the estimated stock price y , in dollars, for a certain company x days after a new product launched, wherMedium · Advanced Math
  30. 30The boiling point of water at sea level is 212 degrees Fahrenheit . For every 550 feet above sea level, the boiling point of water is lowered by about . Which of the following equaMedium · Algebra
  31. 31For the function f defined above, what is the value of ?Medium · Advanced Math
  32. 32Which of the following is the graph in the xy-plane of the given equation?Medium · Advanced Math
  33. 33The function fw=6w2 gives the area of a rectangle, in square feet ft2, if its width is w ft and its length is 6 times its width. Which of the following is the best interpretation Medium · Advanced Math
  34. 34For the function f defined above, what is the value of ?Medium · Algebra
  35. 35x fx -1 10 0 14 1 20 For the quadratic function f , the table shows three values of x and their corresponding values of fx. Which equation defines f ?Medium · Advanced Math
  36. 36An object's kinetic energy, in joules, is equal to the product of one-half the object's mass, in kilograms, and the square of the object's speed, in meters per second. What is the Medium · Advanced Math
  37. 37Some values of the linear function f are shown in the table above. What is the value of ?Medium · Algebra
  38. 38The height, in feet, of an object x seconds after it is thrown straight up in the air can be modeled by the function . Based on the model, which of the following statements best inMedium · Advanced Math
  39. 39In the xy-plane, the points and lie on the graph of which of the following linear functions?Medium · Algebra
  40. 40The graph above shows the distance traveled d, in feet, by a product on a conveyor belt m minutes after the product is placed on the belt. Which of the following equations correctlMedium · Algebra
  41. 41A company's total cost , in dollars, to produce x shirts is given by the function above, where m is a constant and . The total cost to produce 100 shirts is $800. What is the totalMedium · Algebra
  42. 42An engineer wanted to identify the best angle for a cooling fan in an engine in order to get the greatest airflow. The engineer discovered that the function above models the airfloMedium · Advanced Math
  43. 43The function ft=60,0002t410 gives the number of bacteria in a population t minutes after an initial observation. How much time, in minutes, does it take for the number of bacteriaMedium · Advanced Math
  44. 44Time (years) Total amount (dollars) 0 670.00 1 674.02 2 678.06 Sara opened a savings account at a bank. The table shows the exponential relationship between the time t , in yeaMedium · Advanced Math
  45. 45A linear model estimates the population of a city from 1991 to 2015 . The model estimates the population was 57 thousand in 1991 , 224 thousand in 2011 , and x thousand in 2015Medium · Algebra
  46. 46In the linear function f , f0=8 and f1=12. Which equation defines f ?Medium · Algebra
  47. 47fx=2x+244 The given function f represents the perimeter, in centimeters cm, of a rectangle with a length of x cm and a fixed width. What is the width, in cm, of the rectangle?Medium · Algebra
  48. 48w(t)=300-4t The function w models the volume of liquid, in milliliters, in a container t seconds after it begins draining from a hole at the bottom. According to the model, whatMedium · Algebra
  49. 49A certain college had 3,000 students enrolled in 2015. The college predicts that after 2015, the number of students enrolled each year will be 2% less than the number of students eMedium · Advanced Math
  50. 50j(x)=mx+144 For the linear function j , m is a constant and j(12)=18. What is the value of j(10)?Medium · Algebra
  51. 51The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food. If x food calories is equivalent Medium · Algebra
  52. 52The table gives the number of hours, h , of labor and a plumber’s total charge fh, in dollars, for two different jobs. h fh 1 155 3 285 There is a linear relationship betweeMedium · Algebra
  53. 53A rubber ball bounces upward one-half the height that it falls each time it hits the ground. If the ball was originally dropped from a distance of 20.0 feet above the ground, what Medium · Advanced Math
  54. 54The number of bacteria in a liquid medium doubles every day. There are 44,000 bacteria in the liquid medium at the start of an observation. Which represents the number of bacteriaMedium · Advanced Math
  55. 55fx= x 2 - 18 x - 360 If the given function f is graphed in the xy-plane, where y=fx, what is an x-intercept of the graph?Medium · Advanced Math
  56. 56The function f is defined by fx=x+155, and fa=10, where a is a constant. What is the value of a ?Medium · Algebra
  57. 57The function f is defined by fx=7x3. In the xy-plane, the graph of y=gx is the result of shifting the graph of y=fx down 2 units. Which equation defines function g ?Medium · Advanced Math
  58. 58According to Moore's law, the number of transistors included on microprocessors doubles every 2 years. In 1985, a microprocessor was introduced that had 275,000 transistors. Based Medium · Advanced Math
  59. 59The function f is defined by fx=2700.1x. What is the value of f0?Medium · Advanced Math
  60. 60If f(x)=x+7 and g(x)=7x, what is the value of 4f(2)−g(2)?Medium · Algebra