Free Printable Alg2ACP - Intro and Quads Spiral Review

1.

What is x if
f(x) = -2?

a)

4

b)

0

c)

3

d)

8

2.

Given h(x) = 5 - 9x, find h(8).

a)

h(8) = -360

b)

h(8) = -67

3.

If f(x) = x - 5, what is the value of x when f(x) = 15?

a)

20

b)

10

c)

5

d)

0

4.

Which ordered pair below would prevent this table from being a function?

a)

(10, 10)

b)

(2, 4)

c)

(6, 1)

d)

(-2, 0)

5.

Which graph is not a function?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

6.

Find f(-1)

a)

-3

b)

15

c)

19

d)

17

7.

Find f(-3)

a)

-3

b)

15

c)

19

d)

17

8.

If f(x) = 19, Find the value for x.

a)

0

b)

1

c)

2

d)

3

9.

If f(x) = 4, Find the value for x.

a)

0

b)

1

c)

2

d)

3

10.

Find f(1)

a)

1

b)

2

c)

-1

d)

3

11.

Find f(0)

a)

1

b)

2

c)

-1

d)

3

12.

If f(x) = 3 Find the value of x.

a)

2

b)

4

c)

6

d)

0

13.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(3\right)\right)$

a)

34

b)

71

c)

35

d)

142

14.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(-1\right)\right)$

a)

2

b)

15

c)

7

d)

-9

15.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

16.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $f\left(g\left(x\right)\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

17.

Given f and g in the graph,

what is f(f(3)) ?

a)

3

b)

2

c)

4

d)

1

18.

find h(f(-1))

a)

-5

b)

4

c)

-4

d)

12

19.

Find g(f(-2))

a)

-18

b)

-2

c)

1

d)

9

20.

Find h(f(-2))

a)

0

b)

2

c)

-2

d)

26

21.

The line with the equation

y + 1 = -3(x - 5),

contains the point (5, -1)

and has a slope of _______.

a)

-1

b)

1

c)

-3

d)

5

22.

Write the equation in point-slope form

of the line that passes through the point

(4, -7) and has a slope of -1/4.

a)

y + 7 = -1/4(x - 4)

b)

y - 4 = -1/4(x + 7)

c)

y + 7 = 4(x - 4)

d)

y - 7 = -1/4(x - 4)

23.

For the equation

y = 2(x + 4) + 3,

the line has a slope of 2 and contains what point?

a)

(-4, 3)

b)

(3, -4)

c)

(-3, -4)

d)

(-4, -3)

24.

Write the equation of the line in Point-Slope Form.

a)

y=-3/4(x-2)

b)

y=3/5(x-5)+2

c)

y=3/5x-1

d)

y=3/5(x-2)+5

25.

Given the table, what is the equation of the line in point slope form?

a)

y = ½(x - 6) + 12

b)

y = ½(x - 8) + 4

c)

y = ½(x + 4) - 2

d)

y = ½(x +12) - 6

26.

Which is NOT a correct point-slope equation for the line?

a)

y = 1/2(x + 2) + 0

b)

y = 1/2(x - 0) + 1

c)

y = 1/2(x + 2) - 2

d)

y = 1/2(x - 2) + 2

27.

f(x) = -4x - 12

What is f^-1(x)?

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

28.

Which is f ^-1(x)?

a)

f^-1(x) = 5x + 3

b)

f^-1(x) = 5x - 3

c)

f^-1(x) = 5x - 15

d)

f^-1(x) = 1/5(x) + 3/5

29.

Are the following inverses of each other?

a)

True

b)

False

30.

Was the inverse function found correctly?

a)

no,

b)

yes

31.

What is the RANGE?

a)

{-3, 3]

b)

all real numbers

c)

[-4, 5]

d)

[-4, ∞)

32.

What is the DOMAIN?

a)

(4, ∞)

b)

(-4, ∞)

c)

[-3, 3)

d)

(-3, 3]

33.

What is the RANGE?

a)

(-∞, 0)

b)

(0, ∞)

c)

All real numbers

d)

{0, 1, 2, 3, 4,...}

34.

What is the DOMAIN?

a)

[0, ∞)

b)

(-∞, 0)

c)

All real numbers

d)

{0, 1, 2, 3, 4,...}

35.

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

36.

Describe the end behavior of the graph.

a)

x → -∞, f(x) → ∞ and x→∞, f(x) →⁻∞

b)

x → -∞, f(x) → ∞ and x→∞, f(x) →∞

c)

x → -∞, f(x) → ∞ and x→∞, f(x) → 0

d)

x → -∞,f(x) → -∞and x→ ∞, f(x) → ∞

37.

Describe the end behavior of the graph.

a)

x →∞, y→⁻∞ and x →⁻∞,y→⁻∞

b)

x →∞, y→∞ and x→⁻∞, y→∞

c)

x →∞, y→∞ and x→⁻∞, y→0

d)

x →∞,y→∞ and x→⁻∞, y→⁻∞

38.

What is the increasing interval for the function below?

a)

$\left(-\infty,\infty\right)$

b)

$\left(-\infty,2\right]$

c)

$\left(-\infty,6\right]$

d)

$\left(-6,6\right)$

39.

What is/are the increasing interval(s) for the function shown?

a)

$\left(-3,\ 1\right)$

b)

$\left(4,\ 8\right)$

c)

$\left(-\infty,1\right)\ and\ \left(-3,\ 1\right)$

40.

What is/are the decreasing interval(s) for the function shown?

a)

$\left(2,\ 4\right)\ and\ \left(8,\ \infty\right)$

b)

$\left(-\infty,\ 1\right)\ and\ \left(8,\ \infty\right)$

c)

$\left(-\infty,1\right),\ \left(-3,\ 1\right)\ and\ \left(8,\ \infty\right)$

d)

$\left(-\infty,\ 1\right),\ \left(2,\ 4\right)\ and\ \left(8,\ \infty\right)$

41.

What is the decreasing interval(s) on the function shown?

a)

$\left(-7,\ -6\right)\ and\ \left(-2,\ 4\right)$

b)

$\left(-7,\ 0\right)\ and\ \left(-2,\ 4\right)$

c)

$\left(-7,\ -6\right)\ and\ \left(-2,\ 0\right)$

d)

$\left(-7,\ 0\right)\ and\ \left(4,\ 5\right)$

42.

Using the pictured graph, what is f(-3)?

a)

-3

b)

-1

c)

1

d)

3

43.

On the graph, which portion of the piecewise function is represented in red?

a)

x

b)

0.5x + 2.5

c)

-1

d)

0.5x + 2

44.

Match the graph with the correct equation.

a)

b)

c)

d)

45.

Find f(2)

a)

f(2) = 0

b)

f(2) = 1

c)

f(2) = 3

d)

f(2) = 4

46.

a)

A

b)

B

c)

C

d)

D

47.

Describe the transformation that occurred

p(x) = f(x + 3)

a)

Right 3 units

b)

Vertical Stretch

c)

Up 3 units

d)

Left 3 units

48.

Describe the transformation that occurred.

h(x) = f(x) + 2

a)

up 2 units

b)

left 2 units

c)

Vertical Strech

d)

right 2 units

49.

Describe the transformation that occurred

g(x) =2f(x)

a)

Up 2 units

b)

vertical compression

c)

vertical stretch

d)

Right 2 Units

50.

What are the transformations?
y=(x-2)³+4

a)

Horz shift right 2 Vert shift up 4

b)

Horz shift left 2 Vert shift up 4

c)

Horz shift right 2 Vert shift down 4

d)

Horz shift left 2 Vert shift up 4

51.

Describe the transformation of y = g(x) for the function
y = 3g(x - 3) + 5

a)

Shifted up 5 units
Shifted right 3 units
Stretched vertically by a factor of 3

b)

Shifted up 5 units
Shifted left 3 units
Stretched vertically by a factor of 3

c)

Shifted down 5 units
Shifted left 3 units
Stretched vertically by a factor of 3

d)

Shifted down 5 units
Shifted left 3 units
Stretched vertically by a factor of 1/3

52.

Which equation describes the transformation of shifting f(x)=x³ two units right?

a)

x³ + 2

b)

x³ - 2

c)

(x + 2)³

d)

(x - 2)³

53.

Which equation represents the parent quadratic function being vertically stretched by a factor of 2, translated 5 units to the right and translated 3 units down?

a)

$y=2\left(x-5\right)^2-3$

b)

$y=2\left(x+5\right)^2-3$

c)

$y=\frac{1}{2}\left(x+5\right)^2-3$

d)

$y=\frac{1}{2}\left(x-5\right)^2-3$

54.

Which function is graphed?

a)

f(x) = 2|x + 2| -4

b)

f(x) = 2|x - 4| + 2

c)

f(x) = |x + 2| - 4

d)

f(x) = -2|x - 4|

55.

Which function is graphed?

a)

f(x) = 2|x - 5|

b)

f(x) = |x - 5|

c)

f(x) = |x - 5| + 5

d)

f(x) = |x| + 5

56.

What is the equation of the absolute value function?

a)

f(x)= 4|x+3|

b)

f(x)= 1/4 |x+3|

c)

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

d)

f(x)= 4|x - 3|

57.

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

a)

A

b)

B

c)

C

d)

D

58.

What is the vertex of this function?

f\left(x\right)=\left(x+2\right)^2+4

a)

(2, 4)

b)

(-2, 4)

c)

(-4, 2)

d)

(4, 2)

59.

Which of the following describes the extrema of g(x)?

g\left(x\right)=-\left(x-4\right)^2+6

a)

Absolute max of 6 at x = 4

b)

Absolute min of 6 at x = 4

c)

Absolute max of 4 at x = 6

d)

Absolute min of 4 at x = 6

60.

What are the x-intercepts of

f\left(x\right)=x^2-7x+12

?

a)

(3, 0) and (4, 0)

b)

(-3, 0) and (4, 0)

c)

(3, 0) and (-4, 0)

d)

(-3, 0 and (-4,0)

61.

What is the y-intercept of

f\left(x\right)=2\left(x+4\right)^2-17

a)

(0, -17)

b)

(-17, 0)

c)

(0, 15)

d)

(15, 0)

62.

What is the equation of a quadratic function that goes through (3, -7)?

a)

$f\left(x\right)=2\left(x+3\right)^2-7$

b)

$f\left(x\right)\ =\ \frac{1}{2}\left(x-3\right)^2+7$

c)

$f\left(x\right)=3\left(x-3\right)^2-7$

d)

$f\left(x\right)=\left(x+7\right)^2-3$

63.

What is the axis of symmetry of

f\left(x\right)=3x^2+12x-1

?

a)

2

b)

-2

c)

6

d)

-6

64.

Which of these are quadratic?

(select all that apply)

a)

$\left(x-2\right)\left(3x+1\right)$

b)

$4x\left(x^2+7\right)$

c)

$\left(2x-3\right)^2+4$

d)

$4x^3+5y$

65.

What is the axis of symmetry?

f\left(x\right)=3\left(x-1\right)\left(x+7\right)

a)

x = -1

b)

x = 3

c)

x = -3

d)

x = 7

66.

Select all the x-intercepts

f\left(x\right)=-2\left(x+4\right)\left(x-12\right)

a)

(-2, 0)

b)

(-4, 0)

c)

(4, 0)

d)

(-12, 0)

e)

(12, 0)

67.

What is the y-intercept?

f\left(x\right)=\left(x-1\right)\left(x+5\right)

a)

1

b)

-1

c)

5

d)

-5

68.

What is the y-intercept?

g\left(x\right)=-x^2+4x-7

a)

(0, -7)

b)

(0, 4)

c)

(0, -1)

d)

(0, 2)

69.

What is the vertex?

h\left(x\right)=x^2+2x+3

a)

(1, 6)

b)

(-1, 2)

c)

(1, 2)

d)

(-1, 6)

70.

The discriminant is

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

71.

What is the discriminant of 6x² − 2x − 3 = 0

a)

76

b)

29

c)

68

d)

none of these

72.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

73.

Solve by taking square roots:
5b² - 4 = 41

a)

b = 9, b = -9

b)

b = 3, b = -3

c)

b = 8, b = -8

d)

no solutionb

74.

Use the quadratic formula to find the solutions for
y = 3x³ + 8x - 1

a)

0.1167 and -2.7833

b)

.7 and -16.7

c)

.35 and -8.35

d)

0.2358 and -1.236

75.

Simplify √-81

a)

-√81

b)

-9i

c)

9i

d)

81i

76.

Find the sum.
(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

77.

(1-3i)(2+5i)

a)

22-i

b)

16-i

c)

17-i

78.

i^{31}

a)

1

b)

-1

c)

$i$

d)

$-i$

79.

Solve the equation $x^2+8x+20=0$

a)

$-4\pm2i$

b)

$2i\pm4$

c)

$-2\pm4i$

d)

$3\pm2i$

80.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function p= -15x² +600x +60 , where x is the price of each ticket. What is the maximum profit you can make from selling tickets?

a)

$6060

b)

$20

c)

$600

d)

$10,250

81.

A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds.

How much time does it take for the ball to reach its maximum height?

a)

150s

b)

5.5s

c)

2.5s

d)

0s

Alg2ACP - Intro and Quads Spiral Review

Total questions: 81

Worksheet time: 20hrs 15mins

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