Math · Drill 26

Math practice 26

93 questions ~15 min recommended

⏱ 00:00

Score

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1. Given the function $f(x) = x^2 - 3x + 4$, what is the value of $f(-2)$?

A. 2

B. 6

C. 10

D. 14

2. Let $f(x) \= \begin{cases} 2x + 1 & \text{if } x \< 0 \\ x^2 - 3 & \text{if } x \ge 0 \end{cases}$. For how many values of $x$ does $f(x) \= 5$?

A. 0

B. 1

C. 2

D. 3

3. A sequence is defined by $a_1 = 3$ and $a_n = 2a_{n-1} - 1$ for $n \geq 2$. What is $a_5$?

A. 17

B. 23

C. 33

D. 65

4. A model rocket's height in feet after $t$ seconds is modeled by $h(t) = -16t^2 + 96t$. What is the height, in feet, 4 seconds after launch?

A. 128

B. 256

C. 384

D. 512

5. A function is defined by $f(x)=2-x$. What is the value of $f(1-x)$?

A. $$3-x$

B. $$1-x$

C. $$x-1$

D. $$1+x$

6. Which of the following represents $f(x+4)$ if $f(x) = 2x^2 - x$?

A. $$2(x+4)^2 - (x+4)$

B. $$2x^2 + 32x$

C. $$2x^2 + 8x - 4$

D. $$2x^2 + 16x - x$

7. What is $f(-3)$ if $f(x) = 5x^2 - 4x + 1$?

A. 32

B. 42

C. 50

D. 58

8. If $f(x) = 7 - x$, what is $f(3)$?

A. 1

B. 4

C. 5

D. 10

9. What is $f(7)$ if $f(x) = \frac{3x - 1}{2}$?

A. 8

B. 9

C. 10

D. 11

10. A function is defined by $f(x)=x^2+2x-5$. What is $f(-1)$?

A. $$-2$

B. $$-6$

C. $$-8$

D. $$6$

11. If $f(x)=x^2-1$, what is $f(x)+1$?

A. $$x^2$

B. $$(x+1)^2-1$

C. $$x^2+1$

D. $$x^2-2$

12. What is $f(-1)$ if $f(x) = 4x + 3$?

A. -7

B. -1

C. 1

D. 7

13. What is $f(-2)$ if $f(x) = 5x - 2$?

A. -12

B. -8

C. 8

D. 12

14. If $f(x)=\dfrac{x-6}{2}$, what is the value of $f(0)$? Substitute $x=0$: $f(0)=\dfrac{0-6}{2}$.

A. $$0$

B. $$-3$

C. $$-6$

D. $$3$

15. If $f(x)=x^2+4x$, what is the value of $f(2x)$? Substitute $2x$ for every $x$: $f(2x)=(2x)^2+4(2x)$.

A. $$2x^2+8x$

B. $$4x^2+8x$

C. $$4x^2+4x$

D. $$x^2+8x$

16. If $f(x)=x^2-2x+1$, what is $f(-3)$? Substitute $x=-3$: $f(-3)=(-3)^2-2(-3)+1$.

A. $$-2$

B. $$16$

C. $$-14$

D. $$4$

17. Given $f(x)=\dfrac{2x-1}{x+3}$, what is $f(1)$? Substitute $x=1$: $f(1)=\dfrac{2(1)-1}{1+3}$.

A. $$\dfrac{1}{5}$

B. $$\dfrac{2}{4}$

C. $$\dfrac{1}{3}$

D. $$\dfrac{1}{4}$

18. A function is defined by $f(x)=x^2-4x+1$. What is $f(3)$?

A. $$-2$

B. $$-8$

C. $$2$

D. $$4$

19. Which of the following represents $f(x-4)$ if $f(x) = x^2 + x + 1$?

A. $$(x-4)^2 + (x-4) + 1$

B. $$x^2 + x - 16$

C. $$x^2 + 4x + 1$

D. $$x^2 - 8x + 16 + x + 1$

20. A function is defined by $f(x)=3x-7$. What is $f(5)$? Use substitution: $f(x)=3x-7$, so $f(5)=3(5)-7$.

A. $$8$

B. $$-8$

C. $$22$

D. $$-22$

21. Which of the following represents $f(x-2)$ if $f(x) = x^2 + 4x + 4$?

A. $$x^2 + 4x$

B. $$(x-2)^2 + 4(x-2) + 4$

C. $$x^2 - 4x - 4$

D. $$(x-2)^2 + 8x + 4$

22. A function is defined by $f(x)=4-2x$. What is the value of $f(\!-3)$? Show the substitution: $f(x)=4-2x$, so $f(-3)=4-2(-3)$.

A. $$-2$

B. $$-10$

C. $$10$

D. $$2$

23. A function is defined by $f(x)=x^2+4x+4$. What is $f(-2)$?

A. $$16$

B. $$0$

C. $$4$

D. $$-4$

24. A function is defined by $f(x)=\dfrac{x+6}{3}$. What is $f(-3)$?

A. $$1$

B. $$-1$

C. $$3$

D. $$-3$

25. If $f(x) = 9 - 2x$, what is $f(5)$?

A. -3

B. -2

C. -1

D. 1

26. Given the functions $f(x) = 2x^2 + 1$ and $g(x) = x - 3$, what is the value of $f(g(4))$?

A. $$3$

B. $$17$

C. $$9$

D. $$33$

27. If $f(x) = 2x^2 - 3x + 4$, what is $f(0)$?

A. 0

B. 1

C. 2

D. 4

28. Given the function $f(x) = 2x^2 - 3x + 5$, what is the value of $f(-3)$?

A. $$14$

B. $$32$

C. $$41$

D. $$-4$

29. Given the functions $f(x) = x^2 - 1$ and $g(x) = 2x + 3$, what is the value of $f(g(-2))$?

A. $$3$

B. $$0$

C. $$-1$

D. $$8$

30. For the rational function $f(x) = \dfrac{2x + 1}{x - 3}$, which of the following expressions defines the inverse function $f^{-1}(x)$?

A. $$\dfrac{3x - 1}{x + 2}$

B. $$\dfrac{x - 3}{2x + 1}$

C. $$\dfrac{3x + 1}{x - 2}$

D. $$\dfrac{x - 2}{3x + 1}$

31. If $f(x) = \dfrac{3x + 2}{x - 1}$, what is the value of $f^{-1}(5)$?

A. $$\dfrac{1}{2}$

B. $$\dfrac{17}{4}$

C. $$5$

D. $$\dfrac{7}{2}$

32. The table gives values of $f(x)$ and $g(x)$ for $x \= 1$ to $5$. Given $f(g(a)) \= 4$ where $a$ is a positive integer $\le 5$, what is $a$?

A. 1

B. 2

C. 4

D. 5

33. Given $f(x) = x^2 - 4x$ and $g(x) = 2x + 1$, for what real value(s) of $x$ does $f(g(x)) = -3$?

A. $$0$ and $-1$

B. $$-1$ and $1$

C. $$0$ and $1$

D. No real solutions

34. Which of the following represents $f(x + 4)$ if $f(x) = 2x + 3$?

A. 2x + 8

B. 2x + 3

C. 2x + 7

D. 2x + 11

35. If $f(x) = 5x - 10$, what is $f(0)$?

A. -10

B. -5

C. 0

D. 5

36. Given $f(x) = 4x - 7$, which statement is true about $f(x + 2)$?

A. $$f(x + 2) = 4x + 1$

B. $$f(x + 2) = 4x - 7 + 2$

C. $$f(x + 2) = 4x - 3$

D. $$f(x + 2) = 4x + 8$

37. What is $f(-2)$ if $f(x) = x^2 + 3x + 2$?

A. -4

B. 0

C. 4

D. 6

38. What is $f(2)$ if $f(x) = x^3 - 3x^2 + 2x$?

A. 0

B. 2

C. 4

D. 6

39. Given $f(x) = 2x^2 + 3$, which statement is true about $f(x + 1)$?

A. $$f(x + 1) = 2x^2 + 4x + 3$

B. $$f(x + 1) = 2x^2 + 2x + 3$

C. $$f(x + 1) = 2x^2 + 4x + 5$

D. $$f(x + 1) = 2x^2 + 2x + 5$

40. What is the value of $f(-1)$ if $f(x) = x^2 + 2x + 1$?

A. 0

B. 1

C. 2

D. 4

41. If $f(x) = x^2 - 2x + 3$, what is $f(0)$?

A. 0

B. 1

C. 2

D. 3

42. What is the value of $f(5)$ if $f(x) = 3x - x^2$?

A. -10

B. -5

C. 5

D. 10

43. Which of the following represents $f(x + 1)$ if $f(x) = x^2 + 4x$?

A. $$x^2 + 6x + 5$

B. $$x^2 + 2x + 4$

C. $$(x + 1)^2 + 4$

D. $$x^2 + 4x + 5$

44. What is $f(3)$ if $f(x) = 2x + 5$?

A. 7

B. 9

C. 11

D. 15

45. If $f(x) = 8x - 3$, what is $f(4)$?

A. 27

B. 29

C. 32

D. 35

46. What is $f(0)$ if $f(x) = 3x^2 - 7x + 5$?

A. -7

B. -5

C. 0

D. 5

47. If $f(x)=\dfrac{x^2-1}{x-1}$ (for $x\ne1$), what is $f(3)$? $f(x)=\dfrac{x^2-1}{x-1}$, so $f(3)=\dfrac{3^2-1}{3-1}$.

A. $$4$

B. $$\dfrac{9}{2}$

C. $$8$

D. $$2$

48. If $f(x)=x^2+1$, what is the value of $f(2x)$? $f(x)=x^2+1$, so $f(2x)=(2x)^2+1$.

A. $$x^2+2$

B. $$4x+1$

C. $$4x^2+1$

D. $$2x^2+1$

49. Given $f(x)=x^2+2x$, what is the value of $f(2a)$? Show the substitution: $f(x)=x^2+2x$, so $f(2a)=(2a)^2+2(2a)$.

A. $$4a^2+4a$

B. $$4a^2+2a$

C. $$2a^2+4a$

D. $$a^2+4a$

50. A function is defined by $f(x)=5x+2$. What is the value of $f(3)-f(1)$? Use substitution: $f(3)=5(3)+2$ and $f(1)=5(1)+2$.

A. $$8$

B. $$10$

C. $$12$

D. $$5$

51. A function is defined by $f(x)=3x-7$. What is $f(5)$? Show the substitution: $f(x)=3x-7$, so $f(5)=3(5)-7$.

A. $$22$

B. $$-2$

C. $$8$

D. $$3$

52. If $f(x)=\dfrac{2x-1}{3}$, what is $f(x-4)$? Substitute $(x-4)$ for every $x$: $f(x-4)=\dfrac{2(x-4)-1}{3}$.

A. $$\dfrac{2x+7}{3}$

B. $$\dfrac{2x-5}{3}$

C. $$\dfrac{2x-9}{3}$

D. $$\dfrac{2x-1}{3}-4$

53. Given $f(x)=x^2-9$, which statement is true? Use substitution: $f(x+1)=(x+1)^2-9$ and compare to $f(x)+1$.

A. $$f(x+1)=f(x)+1$

B. $$f(x+1)=x^2-10$

C. $$f(x+1)=x^2-8$

D. $$f(x+1)=x^2+2x-8$

54. A function is defined by $f(x)=2x-3$. What is $f(\!-x)$? Show the substitution: $f(x)=2x-3$, so $f(-x)=2(-x)-3$.

A. $$2-x-3$

B. $$-2x-3$

C. $$2x-3$

D. $$-2x+3$

55. A function is defined by $f(x)=x^2-4x+1$. What is $f(-2)$? Show the substitution: $f(x)=x^2-4x+1$, so $f(-2)=(-2)^2-4(-2)+1$.

A. $$-11$

B. $$5$

C. $$-3$

D. $$13$

56. A function is defined by $f(x)=\dfrac{x+2}{x-3}$. What is $f(1)$? Show the substitution: $f(x)=\dfrac{x+2}{x-3}$, so $f(1)=\dfrac{1+2}{1-3}$.

A. $$-\dfrac{1}{2}$

B. $$\dfrac{3}{2}$

C. $$\dfrac{1}{2}$

D. $$-\dfrac{3}{2}$

57. A function is defined by $f(x)=\dfrac{x-1}{2}$. What is $f(7)$?

A. $$\dfrac{7}{2}$

B. $$4$

C. $$\dfrac{5}{2}$

D. $$3$

58. A function is defined by $f(x)=3x^2-2$. What is the value of $f(2)+f(-2)$? Compute using substitution: $f(2)=3(2^2)-2$ and $f(-2)=3((-2)^2)-2$.

A. $$-8$

B. $$20$

C. $$8$

D. $$16$

59. A function is defined by $f(x)=x^2-9$. What is $f(-4)$?

A. $$-25$

B. $$7$

C. $$25$

D. $$-7$

60. A function is defined by $f(x)=4x^2-x$. What is $f(2)$?

A. $$16$

B. $$6$

C. $$12$

D. $$14$

61. A function is defined by $f(x)=x^2+3$. What is the value of $f(x+2)$? Substitute $(x+2)$ for every $x$: $f(x+2)=(x+2)^2+3$.

A. $$x^2+2x+7$

B. $$x^2+2x+5$

C. $$x^2+4$

D. $$x^2+4x+7$

62. A function is defined by $f(x)=x^2-2x$. Which of the following represents $f(x-3)$?

A. $$x^2-6x+9-2x-3$

B. $$x^2-2x-3$

C. $$x^2-6x+9-2x+6$

D. $$x^2-8x+15$

63. A function is defined by $f(x)=x^2-1$. What is the value of $f(\,x+1\,)$?

A. $$x^2+1$

B. $$x^2+2x$

C. $$x^2+2x+2$

D. $$x^2-2x$

64. A function is defined by $f(x)=\dfrac{3}{x-1}$. Which expression equals $f(x+2)$?

A. $$\dfrac{3}{x-1}+2$

B. $$\dfrac{3}{x+1}$

C. $$\dfrac{3}{x-3}$

D. $$\dfrac{3}{x+2}-1$

65. A sequence is defined recursively by a₁ = 3 and aₙ = 2aₙ₋₁ - 4 for n ≥ 2. What is the value of a₅?

A. -12

B. -8

C. -4

D. 4

66. The functions f(x) and g(x) are defined by the tables below. What is the value of f(g(2))?

A. 1

B. 2

C. 3

D. 4

67. What is $f(5)$ if $f(x) = \frac{x}{2} + 4$?

A. 5.5

B. 6.5

C. 7.5

D. 9

68. Given $f(x) = \frac{2x + 3}{x - 1}$, what is $f(2)$?

A. 1

B. 5

C. 7

D. 9

69. Which of the following represents $f(x+1)$ if $f(x) = 4x^2 + x - 1$?

A. $$4x^2 + 3x + 1$

B. $$4x^2 + 4x - 1$

C. $$4(x+1)^2 + (x+1) - 1$

D. $$4x^2 + 5x + 3$

70. Which of the following represents $f(x+3)$ if $f(x) = x^2 - 3x$?

A. $$(x + 3)^2 - 3(x + 3)$

B. $$x^2 + 3x$

C. $$x^2 + 6x + 9 - 3x - 9$

D. $$(x + 3)^2 - 9x$

71. If $f(x) = -x^2 + 3x + 4$, what is $f(1)$?

A. 2

B. 4

C. 6

D. 8

72. If $f(x) = x^2 + 2x + 1$, what is $f(-1)$?

A. -2

B. 0

C. 2

D. 4

73. Which of the following represents $f(x-3)$ if $f(x) = x^2 + 6x + 9$?

A. $$x^2 + 6x$

B. $$x^2 - 6x + 9$

C. $$(x-3)^2 + 12x + 9$

D. $$(x-3)^2 + 6(x-3) + 9$

74. If $f(x)=x^2-4x+1$, what is the value of $f(-2)$?

A. $$-11$

B. $$1$

C. $$-3$

D. $$13$

75. Given $f(x)=5x+2$, which statement is true?

A. $$f(x+1)=f(x)+1$

B. $$f(x+1)=5x+3$

C. $$f(x+1)=f(x)+5$

D. $$f(x+1)=5x+7$

76. A function is defined by $f(x)=\dfrac{10}{x+2}$. What is $f(3)$?

A. $$\dfrac{10}{1}$

B. $$\dfrac{5}{2}$

C. $$\dfrac{10}{5}$

D. $$2$

77. Which of the following represents $f(x + 2)$ if $f(x) = 3x - 1$?

A. 3x + 1

B. 3x + 5

C. 3x + 7

D. 3x + 6

78. A function is defined by $f(x)=7x+2$. What is the value of $f(2x)$?

A. $$14x+2$

B. $$9x$

C. $$7x+4$

D. $$14x+4$

79. What is $f(6)$ if $f(x) = \frac{x}{3} - 2$?

A. -2

B. -1

C. 0

D. 2

80. Given $f(x) = 5x^2 + 2x - 3$, what is the value of $f(0)$?

A. -3

B. 0

C. 2

D. 3

81. If $f(x) = 3x + 8$, what is $f(-2)$?

A. 0

B. 1

C. 2

D. 10

82. If $f(x) = 4x - 5$, what is $f(-3)$?

A. -17

B. -12

C. -7

D. 7

83. A function is defined by $f(x)=5-2x$. What is $f(6)$?

A. $$-17$

B. $$-2$

C. $$-7$

D. $$7$

84. A function is defined by $f(x)=2x+9$. What is $f(-4)$?

A. $$17$

B. $$-17$

C. $$-1$

D. $$1$

85. A function is defined by $f(x)=x^2+1$. Which statement is true? Use substitution to compare $f(x+3)$ and $f(x)+3$.

A. $$f(x+3)=x^2+4$ for all $x$

B. $$f(x)+3=(x+3)^2+1$ for all $x$

C. $$f(x+3)=f(x)+3$ for all $x$

D. $$f(x+3)=(x+3)^2+1$ for all $x$

86. If $f(x) = 2x^2 - x + 1$, what is $f(0)$?

A. -1

B. 0

C. 1

D. 2

87. Which of the following represents $f(x+2)$ if $f(x) = x^2 + 3x + 1$?

A. $$(x+2)^2 + 3(x+2) + 1$

B. $$x^2 + 7x + 7$

C. $$x^2 + 2x + 4$

D. $$x^2 + 5x + 1$

88. If $f(x)=2x^2+5$, which of the following represents $f(x+3)$? Substitute $(x+3)$ for every $x$: $f(x+3)=2(x+3)^2+5$.

A. $$2x^2+12x+23$

B. $$2x^2+5x+8$

C. $$2x^2+11$

D. $$2x^2+8x+23$

89. If $f(x) = 2x^2 - 5x + 4$, what is $f(3)$?

A. 7

B. 8

C. 10

D. 13

90. Which of the following represents $f(x-1)$ if $f(x) = 6x + 2$?

A. 6x - 6

B. 6x - 4

C. 6x - 10

D. 6x + 2

91. Given the function $f(x) = 2x^2 - 3x + 5$, what is the value of $f(-3)$?

A. $$41$

B. $$14$

C. $$32$

D. $$-4$

92. For the rational function $f(x) = \dfrac{2x + 1}{x - 3}$, which of the following expressions defines the inverse function $f^{-1}(x)$?

A. $$\dfrac{3x + 1}{x - 2}$

B. $$\dfrac{x - 2}{3x + 1}$

C. $$\dfrac{3x - 1}{x + 2}$

D. $$\dfrac{x - 3}{2x + 1}$

93. Given the functions $f(x) = x^2 - 1$ and $g(x) = 2x + 3$, what is the value of $f(g(-2))$?

A. $$3$

B. $$0$

C. $$-1$

D. $$8$

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