Log inSign up free
Back to Math

Nonlinear Functions

Math · Advanced Math · 132 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 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
  3. 3The 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
  4. 4All 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
  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. 7Moving 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
  8. 8Time (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
  9. 9Function 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
  10. 10The 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
  11. 11The function f is defined by f(x)=4+x. What is the value of f144?Easy · Advanced Math
  12. 12A 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
  13. 13A 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
  14. 14The 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
  15. 15The 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
  16. 16The 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
  17. 17A 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
  18. 18The 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
  19. 19fx=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
  20. 20The 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
  21. 21In 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
  22. 22fx= 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
  23. 23In 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
  24. 24The 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
  25. 25The 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
  26. 26A 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
  27. 27A 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
  28. 28A 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
  29. 29y = 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
  30. 30The function f is defined by fx=16x. What is the value of fx when x = 3 ?Easy · Advanced Math
  31. 31Function 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
  32. 32gx=x2+55 What is the minimum value of the given function?Medium · Advanced Math
  33. 33fx= 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
  34. 34Moving 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
  35. 35The 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
  36. 36fx=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
  37. 37Immanuel 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
  38. 38A 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
  39. 39fx=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
  40. 40From 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
  41. 41If 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
  42. 42For the first curve: Moving 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 3). In quadrant 1,Easy · Advanced Math
  43. 43Moving 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
  44. 44f(x)=(x+6)(x+5)(x-4) The function f is given. Which table of values represents y=f(x)-3?Medium · Advanced Math
  45. 45The 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
  46. 46fx=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
  47. 47In 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
  48. 48y = 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
  49. 49For the function f defined above, what is the value of ?Medium · Advanced Math
  50. 50Which of the following is the graph in the xy-plane of the given equation?Medium · Advanced Math
  51. 51If , what is ?Easy · Advanced Math
  52. 52The 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
  53. 53The 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
  54. 54x 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
  55. 55ft=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
  56. 56For the function f defined above, what is the value of ?Easy · Advanced Math
  57. 57An 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
  58. 58In 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
  59. 59Moving 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 8). In quadrant 1, the curve trends up shEasy · Advanced Math
  60. 60The 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