Log inSign up free
Back to Math

Linear Functions

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

Practice this skill
DifficultyAllEasyMediumHard
  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 total cost f(x), in dollars, to lease a car for 36 months from a particular car dealership is given by f(x)=36x+1,000, where x is the monthly payment, in dollars. What is theEasy · Algebra
  3. 3A window repair specialist charges $220 for the first two hours of repair plus an hourly fee for each additional hour. The total cost for 5 hours of repair is $400. Which functionHard · Algebra
  4. 4The 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
  5. 5An economist modeled the demand Q for a certain product as a linear function of the selling price P. The demand was 20,000 units when the selling price was $40 per unit, and the deHard · Algebra
  6. 6The quadratic function h is defined as shown. In the xy-plane, the graph of intersects the x-axis at the points and , where t is a constant. What is the value of t ?Hard · Advanced Math
  7. 7The function f is defined by f(x)=(-8)(2)x+22. What is the y-intercept of the graph of y=f(x) in the xy-plane?Hard · Advanced Math
  8. 8All values are approximate. The parabola opens downward. The vertex of the parabola is at (0.6 comma 5.5). The parabola passes through the following points: (0.0 comma 3.8) (0.6 cEasy · Advanced Math
  9. 9fx=9,0000.66x The given function f models the number of advertisements a company sent to its clients each year, where x represents the number of years since 1997, and 0≤x≤5. If Hard · Advanced Math
  10. 10The first term of a sequence is 9 . Each term after the first is 4 times the preceding term. If w represents the n th term of the sequence, which equation gives w in terms of n Hard · Advanced Math
  11. 11The cost of renting a backhoe for up to 10 days is $270 for the first day and $135 for each additional day. Which of the following equations gives the cost y , in dollars, of reHard · Algebra
  12. 12The front of a roller-coaster car is at the bottom of a hill and is 15 feet above the ground. If the front of the roller-coaster car rises at a constant rate of 8 feet per second, Easy · Algebra
  13. 13According 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
  14. 14Moving from left to right: The curve passes from quadrant 3 to quadrant 4. In quadrant 3, the curve trends up sharply to point (0 comma negative 5). In quadrant 4, the curve trendEasy · Advanced Math
  15. 15Time (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
  16. 16Function f is defined by fx=-ax+b, where a and b are constants. In the xy-plane, the graph of y=fx-12 has a y-intercept at 0,-757. The product of a and b is 320 7 . What iHard · Advanced Math
  17. 17If f is the function defined by , what is the value of ?Easy · Algebra
  18. 18The parabola opens upward. The parabola passes through the following points: (0 comma 0) (3 comma negative 12) (6 comma 0) Scientists recorded data about the ocean water levels aEasy · Advanced Math
  19. 19d = 16 t The given equation represents the distance d , in inches, where t represents the number of seconds since an object started moving. Which of the following is the bEasy · Algebra
  20. 20f(x)=39 For the given linear function f , which table gives three values of x and their corresponding values of fx?Medium · Algebra
  21. 21The function f is defined by f(x)=4+x. What is the value of f144?Easy · Advanced Math
  22. 22A 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
  23. 23The function g is defined by gx=6x. For what value of x is g(x)=54 ?Easy · Algebra
  24. 24A machine launches a softball from ground level. The softball reaches a maximum height of 51.84 meters above the ground at 1.8 seconds and hits the ground at 3.6 seconds. Which Hard · Advanced Math
  25. 25The function f is defined by f(x)=ax+b, where a and b are constants. In the x y -plane, the graph of y=fx has an x -intercept at 2,0 and a y -intercept at 0,-323. What is thHard · Advanced Math
  26. 26In 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
  27. 27The 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
  28. 28The number y is 84 less than the number x . Which equation represents the relationship between x and y ?Easy · Algebra
  29. 29The revenue , in dollars, that a company receives from sales of a product is given by the function f above, where x is the unit price, in dollars, of the product. The graph of in tHard · Advanced Math
  30. 30The function f is defined by the equation fx=7x+2. What is the value of fx when x = 4 ?Easy · Algebra
  31. 31A culture of bacteria is growing at an exponential rate, as shown in the table above. At this rate, on which day would the number of bacteria per milliliter reach ?Hard · Advanced Math
  32. 32The 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
  33. 33fx=ax2+4x+c In the given quadratic function, a and c are constants. The graph of y=fx in the xy-plane is a parabola that opens upward and has a vertex at the point h,k, where h Hard · Advanced Math
  34. 34The parabola opens upward. The vertex is at point (7 comma 0). The parabola passes through the following points: (6 comma 3) (7 comma 0) (8 comma 3) The x-intercept of the graph Easy · Advanced Math
  35. 35In 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
  36. 36A 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
  37. 37fx= 4 x 2 + 64 x + 262 The function g is defined by gx=fx+5. For what value of x does gx reach its minimum?Hard · Advanced Math
  38. 38In 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
  39. 39The table shown includes some values of x and their corresponding values of y. Which of the following graphs in the xy-plane could represent the relationship between x and y ?Easy · Advanced Math
  40. 40The function f is defined by fx= x - 6 x - 2 x + 6 . In the xy-plane, the graph of y=gx is the result of translating the graph of y=fx up 4 unitHard · Advanced Math
  41. 41The function g is defined by . What is the value of ?Easy · Algebra
  42. 42A 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
  43. 43A 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
  44. 44A quadratic function models a projectile's height, in meters, above the ground in terms of the time, in seconds, after it was launched. The model estimates that the projectile was Hard · Advanced Math
  45. 45y = x 2 - 14 x + 22 The given equation relates the variables x and y . For what value of x does the value of y reach its minimum?Hard · Advanced Math
  46. 46The function f is defined by fx=4x. For what value of x does fx=8?Easy · Algebra
  47. 47The function f is defined by fx=16x. What is the value of fx when x = 3 ?Easy · Advanced Math
  48. 48Function f is defined by fx=-ax+b, where a and b are constants. In the xy-plane, the graph of y=fx-15 has a y-intercept at 0,-997. The product of a and b is 65 7 . What isHard · Advanced Math
  49. 49According to the graph, what is the cost for each additional mile traveled, in dollars, of a cab ride?Easy · Algebra
  50. 50The 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
  51. 51gx=x2+55 What is the minimum value of the given function?Medium · Advanced Math
  52. 52fx= x - 14 x + 19 The function f is defined by the given equation. For what value of x does fx reach its minimum?Hard · Advanced Math
  53. 53Fx=95x-273.15+32 The function F gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of x kelvins. If a temperature increased by 9.10 kelvins, by howHard · Algebra
  54. 54Moving from left to right: The curve passes from quadrant 2 to quadrant 1. In quadrant 2, the curve trends up gradually to point (0 comma 2). In quadrant 1, the curve trends up shEasy · Advanced Math
  55. 55The 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
  56. 56x 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
  57. 57The parabola opens upward. The vertex is at point (4 comma 0). The parabola passes through the following points: (3 comma 5) (4 comma 0) (5 comma 5) What is the x-intercept of thEasy · Advanced Math
  58. 58fx=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
  59. 59The 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
  60. 60Immanuel 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