Free Printable A2T: Unit 1 & 2 Review

1.

What is the value of the function at g(4)?

a)

5

b)

1

c)

0

d)

Not enough information

2.

Find all x values when g(x)=6.

a)

x=3

b)

x=3 or x=6

c)

x=-4 or x=3

d)

x=-4

3.

What is f(2)?

a)

-4

b)

8

c)

0

d)

5

4.

Which of the following situations could be descried by the equation y=120-25x?

a)

There are 120 people in the football stadium, and 25 more are entering each hour.

b)

A plumber charges $25 for a house call and $120 per hour.

c)

A teacher has 120 students. Her third period has 25 students

d)

There are 120 gallons of water in a tank. It releases water at a rate of 25 gallons per minute

5.

Find the inverse of
f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

6.

Find the inverse of the function

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

7.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))

a)

-42

b)

-26

c)

-18

d)

None of these.

8.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

9.

Which graph matches the function:
y = -2|x - 3| + 5

a)

A

b)

B

c)

C

d)

D

10.

What is the domain and range of the graph?

a)

Domain: x ≤ 3
Range: all real numbers

b)

Domain: all real numbers
Range: all real numbers

c)

Domain: all real numbers
Range: y ≤ 3

d)

Domain: all real numbers
Range: y ≥ 3

11.

Describe the transformations of the absolute value equation.

a)

Reflects over x-axis, compresses wider, shifts right 1 unit

b)

Reflects over x-axis, compresses wider, shifts up 1 unit

c)

Reflects over x-axis, stretches more narrow, shifts right 1 unit

d)

Reflects over x-axis, stretches more narrow, shifts up 1 unit

12.

Perform the indicated operation.

a)

b)

c)

d)

13.

Perform the indicated operation.

a)

b)

c)

d)

14.

Complete the operation and evaluate.

a)

b)

c)

d)

15.

Perform the indicated operation.

a)

b)

c)

d)

16.

Perform the indicated operation and evaluate for the given value.

a)

b)

c)

d)

17.

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

a)

Left 3 and up 5

b)

Right 3 and down 5

c)

Left 3 and down 5

d)

Right 3 and up 5

18.

Which equation shows a function that is translated left 4 and 7 up?

a)

y = |x + 4| + 7

b)

y = (x - 4)² + 7

c)

y = (x + 7)² - 4

d)

y = |x + 4| - 7

19.

What is the domain of y = $\sqrt{x\ +\ 2}$

a)

All real numbers

b)

All real numbers except $-2$

c)

All real number greater than or equal to $-2$

d)

All real numbers greater than $-2$

20.

$Evaluate\ the\ function\ for\ f\left(-9\right)\ if\ f\left(x\right)=\frac{3}{5}x+8$

a)

$\frac{67}{5}$

b)

$-\frac{13}{5}$

c)

$-\frac{67}{5}$

d)

$\frac{13}{5}$

21.

$Given\ g\left(x\right)=20x-189\ what\ is\ g\left(\frac{1}{2}\right)?$

a)

-189

b)

-179

c)

200

d)

answer not here

22.

$Given\ g\left(x\right)=6x-19\ what\ is\ g\left(25\right)?$

a)

130

b)

131

c)

119

d)

answer not here

23.

$Given\ f\left(x\right)=\frac{3}{2}x+5\ what\ is\ f\left(12\right)?$

a)

$\frac{43}{2}$

b)

$20$

c)

$23$

d)

$5$

24.

$Given\ f\left(x\right)=6x-10\ what\ is\ f\left(120\right)$

a)

$-10$

b)

$-4$

c)

$120$

d)

$710$

25.

$Given\ f\left(x\right)=\frac{1}{3}\left(x+6\right)\ what\ is\ f\left(-6\right)?$

a)

$\frac{2}{3}$

b)

$-8$

c)

$-6$

d)

0

26.

$Given\ f\left(x\right)=2x-10\ for\ which\ value\ of\ x\ that\ f\left(x\right)=-10?$

a)

-1

b)

0

c)

2

d)

3

27.

$Given\ f\left(x\right)=2x-10\ for\ which\ value\ of\ x\ that\ f\left(x\right)=-12?$

a)

-1

b)

0

c)

2

d)

3

28.

$Given\ f\left(x\right)=2x-10\ for\ which\ value\ of\ x\ that\ f\left(x\right)=-34?$

a)

4

b)

10

c)

-5

d)

-12

29.

$Given\ f\left(x\right)=2x-10\ for\ which\ value\ of\ x\ that\ f\left(x\right)=8?$

a)

5

b)

10

c)

9

d)

-12

30.

What is f(2)?

a)

-4

b)

8

c)

0

d)

5

31.

What is the value of f(-5)?

a)

-2

b)

2

c)

4

d)

0

32.

Find g(4)

a)

g(4) = 4

b)

g(4) = -4

c)

g(4) = 2

d)

g(2) = 4

33.

f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)

a)

16

b)

4

c)

-4

d)

None of these.

34.

Given f(x) = 2x and g(x) = x²+3 , find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

35.

If f(x) = x² and g(x) = 3x - 1, find f(g(x))

a)

9x² - 6x + 1

b)

3x - 1

c)

3x² - 1

d)

9x² - 1

36.

Given f(x) = 3x + 10
and g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

37.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of f(g(4)).

a)

182

b)

40

c)

61

d)

None of the Above

38.

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

a)

(1, 2) (3, 8) (-3, 6)

b)

(1, 2) (8, 3) (-3, 6)

c)

(-1, -2) (-3, -8) (3, -6)

d)

(2, 1) (8, 3) (6, -3)

39.

What is the inverse of the points
(1,3)(2,4)(6,8)

a)

(3,1)(4,2)(8,6)

b)

(-3,-1)(-4,-2)(-8,-6)

c)

(1,3)(2,4)(6,8)

d)

(-1,-3)(-2,-4)(-6,-8)

40.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

41.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

42.

Are the following inverses of each other?

a)

True

b)

False

43.

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

a)

Left 3 and up 5

b)

Right 3 and down 5

c)

Left 3 and down 5

d)

Right 3 and up 5

44.

Identify the transformation from the graph of f(x)=x²to the graph g(x)= -(x+5)²

a)

shifted up five units

reflection in x-axis

b)

shifted down five units

reflection in x-axis

c)

shifted left 5 units

reflection x-axis

d)

shifted right 5 units

reflection x-axis

45.

Describe the transformations that maps
y = g(x) to y = - g(x + 6) - 10

a)

Reflect over y-axis
Shifted down 10 units
Shifted left 6 units

b)

Reflect over x-axis
Shifted up 10 units
Shifted left 6 units

c)

Reflect over y-axis
Shifted up 10 units
Shifted right 6 units

d)

Reflect over x-axis
Shifted down 10 units
Shifted left 6 units

46.

Factor the quadratic expression completely.
x² - 5x + 6

a)

(x - 3)(x - 2)

b)

(x + 3)(x - 2)

c)

(x + 6)(x - 1)

d)

(x - 6)(x + 1)

47.

Factor the quadratic expression completely.
x² - 121

a)

(x - 11)(x - 11)

b)

(x + 11)(x - 11)

c)

(x + 5)(x - 20)

d)

(x - 121)(x + 121)

48.

Factor the quadratic expression completely.
4x² + 19x + 12

a)

(4x + 3)(x + 4)

b)

(x + 3)(4x + 4)

c)

(x + 4)(4x - 3)

d)

(x - 4)(4x - 3)

49.

Identify the vertex.

f(x)=x² + 4x + 7

a)

(-2, 3)

b)

(2, 3)

c)

(4, 7)

d)

(-4, 3)

50.

Simplify the radical expression:

a)

b)

c)

d)

51.

Simplify the radical expression:

a)

b)

c)

d)

52.

Perform the operation and simplify the radical completely:

a)

b)

c)

d)

53.

Simplify the radical expression completely:

a)

b)

c)

d)

54.

Solve: x²+ 8x = 65

a)

x = 5 or -13

b)

x = 13 or -5

c)

x = 5 or 13

d)

x = -13 or -5

55.

Solve: 2(x - 4)² + 7 = 105

a)

x = 4 or 7

b)

x = 3 or 11

c)

x = 11 or -3

d)

x = 4 or -7

56.

What is the sum of the solutions to the quadratic equation: x² + 9x = -20

a)

-1

b)

-5

c)

-9

d)

-20

57.

Solve: x² - 19 = 62

a)

x = 9

b)

x = -9

c)

x = 9 or -9

d)

x = 43

58.

Solve:

a)

b)

c)

d)

59.

Solve: 3x² + 192 = 0

a)

x = 8i

b)

x = 8i or -8i

c)

x = 8 or -8

d)

x = 8

60.

Solve: 1/3(x - 5)² + 9 = -3

a)

x = 5 ± 6i

b)

x = 5i ± 6

c)

x = 11 or -1

d)

x = 6i ± 5

61.

How many solutions does the quadratic equation x² + 8x + 15 = 0 have?

a)

Two real solutions

b)

One real solution

c)

Two complex (imaginary) solutions

d)

No solution

62.

Which of the following graphs could represent a quadratic function with a discriminant of -16?

a)

b)

c)

d)

None of these

63.

Choose all statements that are true about the graph.

a)

The graph has a maximum at (1, 4)

b)

The graph represents the function f(x) = - (x-1)² - 4

c)

The function x² + 7x + 4 has a greater y-intercept

d)

If (-3, -18) is on the graph then, (4, -18) is also on the graph.

64.

Simplify the following radical: √32

a)

3√2

b)

4√8

c)

16√2

d)

4√2

65.

a)

-5√1

b)

8√2 + 13√3

c)

21√5

d)

20√5

66.

a)

17√2

b)

9√1

c)

9

d)

9√2

67.

a)

13√3

b)

10√30

c)

13√6

d)

11√3

68.

Simplify:

a)

1/5

b)

20/100

c)

2/10

d)

1/√25

69.

Divide:

a)

√12

b)

(4√3)/3

c)

√3

d)

(2√3)/3

70.

a)

A

b)

B

c)

C

d)

D

71.

Simplify.

a)

-5i

b)

5

c)

5i

d)

-5

72.

√(-300)

a)

10i√3

b)

15√15

c)

-10√3

d)

2i√13

73.

(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

74.

(2i)(3i)

a)

5i

b)

-5

c)

6i

d)

-6

75.

Simplify:
-3i(4 + 2i)

a)

6 - 12i

b)

6 + 12i

c)

-12i - 6i²

d)

-12i + 6i²

76.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

77.

What is the simplified form of the above?

a)

7/10 + 11/10 i

b)

13/10 +1/10 i

c)

5/4 - 3/2i

d)

7/10 - 11/10 i

78.

a)

b)

c)

d)

79.

Simplify
$\left(15-2i\right)-\left(3+5i\right)$

a)

$12-7i$

b)

$-12-7i$

c)

$12+7i$

d)

$-12+7i$

80.

Simplify
$\left(2+7i\right)+\left(-11-6i\right)$

a)

$-9+i$

b)

$-9-i$

c)

$9+i$

d)

$9-i$

A2T: Unit 1 & 2 Review

Total questions: 80

Worksheet time: 1hrs 20mins

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