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Linear Functions

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

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  1. 1A 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
  2. 2An 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
  3. 3The 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
  4. 4The 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
  5. 5fx=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
  6. 6The 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
  7. 7The 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
  8. 8Function 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
  9. 9A 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
  10. 10The 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
  11. 11The 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
  12. 12A 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
  13. 13fx=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
  14. 14fx= 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
  15. 15The 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
  16. 16A 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
  17. 17y = 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
  18. 18Function 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
  19. 19fx= 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
  20. 20Fx=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
  21. 21A model estimates that at the end of each year from 2015 to 2020, the number of squirrels in a population was 150 % more than the number of squirrels in the population at the end oHard · Advanced Math
  22. 22fx=59-2x The function f is defined by the given equation. For which of the following values of k does fk=3k?Hard · Advanced Math
  23. 23The functions f and g are defined as f(x)= 1 4 x - 9 and g(x)= 3 4 x + 21 . If the function h is defined as h(x)=f(x)+g(x), what is the x-coordinate of the x-inteHard · Algebra
  24. 24If during this time the population of the city decreases by a fixed percent each year, which of the following must be true?Hard · Advanced Math
  25. 25The constant 2.74 in this function estimates which of the following?Hard · Algebra
  26. 26fx=5,4700.64x12 The function f gives the value, in dollars, of a certain piece of equipment after x months of use. If the value of the equipment decreases each year by p% of itsHard · Advanced Math
  27. 27The function fx=19x-72+3 gives a metal ball's height above the ground fx, in inches, x seconds after it started moving on a track, where 0≤x≤10. Which of the following is the bestHard · Advanced Math
  28. 28ft=8,0000.65t The given function f models the number of coupons a company sent to their customers at the end of each year, where t represents the number of years since the end oHard · Advanced Math
  29. 29In the xy-plane, a parabola has vertex (9,-14) and intersects the x-axis at two points. If the equation of the parabola is written in the form y = a x 2 + b x Hard · Advanced Math
  30. 30x fx 1 -64 2 0 3 64 For the linear function f , the table shows three values of x and their corresponding values of fx. Function f is defined by fx=ax+b, where a and b Hard · Algebra
  31. 31The table above gives selected values of a polynomial function p. Based on the values in the table, which of the following must be a factor of p ?Hard · Advanced Math
  32. 32Oil and gas production in a certain area dropped from 4 million barrels in 2000 to 1.9 million barrels in 2013. Assuming that the oil and gas production decreased at a constant ratHard · Algebra
  33. 33When the quadratic function f is graphed in the xy-plane, where y=fx, its vertex is -3,6. One of the x-intercepts of this graph is -174,0. What is the other x-intercept of the graHard · Advanced Math
  34. 34The function f is defined by . The graph of f in the xy-plane is a parabola. Which of the following intervals contains the x-coordinate of the vertex of the graph of f ?Hard · Advanced Math
  35. 35One gallon of paint will cover 220 square feet of a surface. A room has a total wall area of w square feet. Which equation represents the total amount of paint P , in gallons, neHard · Algebra
  36. 36A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the Hard · Advanced Math
  37. 37Pt=2901.0446t The function P models the population, in thousands, of a certain city t years after 2005 . According to the model, the population is predicted to increase by n% evHard · Advanced Math
  38. 38For the function f , f0=86, and for each increase in x by 1 , the value of fx decreases by 80%. What is the value of f2?Hard · Advanced Math
  39. 39The equation above models the number of members, M, of a gym t years after the gym opens. Of the following, which equation models the number of members of the gym q quarter years aHard · Advanced Math
  40. 40Fx=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 2.10 kelvins, by howHard · Algebra
  41. 41The functions f and g are defined by the given equations, where x≥0. Which of the following equations displays, as a constant or coefficient, the maximum value of the function itHard · Advanced Math
  42. 42Square P has a side length of x inches. Square Q has a perimeter that is 176 inches greater than the perimeter of square P. The function f gives the area of square Q, in square Hard · Advanced Math
  43. 43The surface area of a cube is , where a is a positive constant. Which of the following gives the perimeter of one face of the cube?Hard · Advanced Math
  44. 44The function h is defined by h(x)=ax+b, where a and b are positive constants. The graph of y=h(x) in the x y -plane passes through the points (0 , 10 ) and (-2 , 325 36 Hard · Advanced Math
  45. 45x y 21 -8 23 8 25 -8 The table shows three values of x and their corresponding values of y , where y=fx+4 and f is a quadratic function. What is the y-coordinate of the yHard · Advanced Math
  46. 46The table above shows some values of x and their corresponding values for the linear function f. What is the x-intercept of the graph of in the xy-plane?Hard · Algebra
  47. 47A quadratic function models the height, in feet, of an object above the ground in terms of the time, in seconds, after the object is launched off an elevated surface. The model indHard · Advanced Math
  48. 48Function f is defined by fx=x+6x+5x+1. Function g is defined by gx=fx-1. The graph of y=gx in the xy-plane has x-intercepts at a,0, b,0, and c,0, where a , b , and c are distincHard · Advanced Math
  49. 49The total distance d, in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of t, where t is the time in secondHard · Advanced Math
  50. 50fx= 4 x 2 - 50 x + 126 The given equation defines the function f . For what value of x does fx reach its minimum?Hard · Advanced Math
  51. 51The function h is defined above, where a, b, and c are integer constants. If the zeros of the function are 6, and 7, what is the value of c ?Hard · Advanced Math
  52. 52The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food. If the 180 food calories in a graHard · Algebra
  53. 53fx=9(4)x The function f is defined by the given equation. If g(x)=f(x+2), which of the following equations defines the function g ?Hard · Advanced Math
  54. 54An object hangs from a spring. The formula relates the length , in centimeters, of the spring to the weight w, in newtons, of the object. Which of the following describes the meaniHard · Algebra
  55. 55fx= x + 7 2 + 4 The function f is defined by the given equation. For what value of x does fx reach its minimum?Hard · Advanced Math
  56. 56For the function f, if for all values of x, what is the value of ?Hard · Algebra
  57. 57Kao measured the temperature of a cup of hot chocolate placed in a room with a constant temperature of 70 degrees Fahrenheit (°F). The temperature of the hot chocolate was 185°F atHard · Advanced Math
  58. 58pt=90,0001.06t The given function p models the population of Lowell t years after a census. Which of the following functions best models the population of Lowell m months afterHard · Advanced Math
  59. 59The population of a town is currently 50,000, and the population is estimated to increase each year by 3% from the previous year. Which of the following equations can be used to esHard · Advanced Math
  60. 60For the exponential function f , the value of f1 is k , where k is a constant. Which of the following equivalent forms of the function f shows the value of k as the coefficient Hard · Advanced Math