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Nonlinear Functions

Math · Advanced Math · 132 questions · every one comes with a full explanation.

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  1. 1The 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
  2. 2The 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
  3. 3fx=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
  4. 4The 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
  5. 5Function 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
  6. 6A 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
  7. 7The 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
  8. 8The 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
  9. 9A 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
  10. 10fx=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
  11. 11fx= 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
  12. 12The 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
  13. 13A 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
  14. 14y = 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
  15. 15Function 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
  16. 16fx= 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
  17. 17A 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
  18. 18fx=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
  19. 19If 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
  20. 20fx=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
  21. 21The 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
  22. 22ft=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
  23. 23In 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
  24. 24The 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
  25. 25When 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
  26. 26The 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
  27. 27A 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
  28. 28Pt=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
  29. 29For 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
  30. 30The 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
  31. 31The 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
  32. 32Square 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
  33. 33The 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
  34. 34The 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
  35. 35x 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
  36. 36A 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
  37. 37Function 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
  38. 38The 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
  39. 39fx= 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
  40. 40The 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
  41. 41fx=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
  42. 42fx= 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
  43. 43Kao 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
  44. 44pt=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
  45. 45The 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
  46. 46For 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
  47. 47The quadratic function above models the height above the ground h, in feet, of a projectile x seconds after it had been launched vertically. If is graphed in the xy-plane, which ofHard · Advanced Math
  48. 48For the exponential function f, the table above shows several values of x and their corresponding values of , where a is a constant greater than 1. If k is a constant and , what isHard · Advanced Math
  49. 49Moving from left to right: The curve is in quadrant 3. The curve trends down sharply. As x increases, the curve approaches the line x equals negative 4. As x decreases, the curveHard · Advanced Math
  50. 50fx= x - 10 x + 13 The function f is defined by the given equation. For what value of x does fx reach its minimum?Hard · Advanced Math
  51. 51For the function q , the value of qx decreases by 45 % for every increase in the value of x by 1 . If q0=14, which equation defines q ?Hard · Advanced Math
  52. 52Two variables, x and y , are related such that for each increase of 1 in the value of x , the value of y increases by a factor of 4 . When x = 0 , y = 200 . Which equaHard · Advanced Math
  53. 53What is the minimum value of the function f defined by ?Hard · Advanced Math
  54. 54Let the function p be defined as , where c is a constant. If , what is the value of ?Hard · Advanced Math