Free Printable 1st Semester Algebra II Concepts Review

1.

What is the DOMAIN of this linear function?

a)

$\left[-6,\ 6\right]$

b)

$\left[0,\ 6\right]$

c)

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

d)

No Solution

2.

What is the RANGE of this linear function?

a)

-6 ≤ y ≤ 6

b)

0 ≤ y ≤ 6

c)

2 ≤ y ≤ 8

d)

4 ≤ y ≤ 3

3.

What is the DOMAIN of the function graphed on the grid?

a)

-4 ≤ x < 5

b)

-4 ≤ x ≤ 5

c)

-3 ≤ x < 3

d)

-3 < x ≤ 3

4.

What is the RANGE?

a)

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

b)

$\left[-10,\ 6\right]$

c)

$\left[-10,\ \infty\right)$

d)

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

5.

What is the x-intercept?

a)

12

b)

-3

c)

8

d)

0

6.

What is the y-intercept?

a)

12

b)

-3

c)

8

d)

0

7.

Find the x and y intercepts
4x - 5y = 40

a)

x intercept is 10
y intercept is 8

b)

x intercept is 10
y intercept is 20

c)

x intercept is 8
y intercept is 10

d)

x intercept is 10
y intercept is -8

8.

What is the maximum value?

a)

5

b)

0

c)

-5

d)

2

9.

Determine end behavior of function with the given graph

a)

$x\rightarrow-\infty;\ f\left(x\right)\ \rightarrow\ -\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

b)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow\ -\infty$

d)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

10.

Where is this graph increasing or decreasing?

a)

Increasing: $\left(-7,\ -3\right)$

Decreasing: $\left(-7,\ 2\right)$

b)

Increasing: $\left(0,\ 2\right)$

Decreasing: $\left(-3,\ 0\right)$

c)

Increasing: $\left(-3,\ 0\right)$

Decreasing: $\left(0,\ 2\right)$

d)

Increasing: $\left(-7,\ 2\right)$

Decreasing: $\left(-7,\ -3\right)$

11.

Label the transformations that a, b, c, & d represent in a function.

a)Vertical Stretch/Shrink

b)Vertical Shift

c)Horizontal Stretch/Shrink

d)Horizontal Shift

1

2

3

4

1)

2)

3)

4)

12.

What are the following transformations?

g(x) = - (x+2)

a)

reflection over the y axis and 2 units to the right

b)

reflection over the x axis and 2 units right

c)

reflection over the y axis and 2 units left

d)

reflection over the x axis and 2 units left

13.

What are the following transformations:
g(x) = f(-x) - 4

a)

reflection over the x axis and 4 units right

b)

reflection over the x axis and 4 units down

c)

reflection over the y axis and 4 units right

d)

reflection over the y axis and 4 units down

14.

If the blue is y=x^2,the red must be

a)

y=(x+3)²

b)

y=(x-3)²

c)

y=x²+3

d)

y=x²-2

15.

Even, odd, or neither?

a)

Even

b)

Odd

c)

Neither

16.

Is the graph an even, odd, or neither function?

a)

Even

b)

Odd

c)

Neither

17.

The red graph shows the graph of y=f(x)

Identify the blue graph...

a)

y = f(x - 3)

b)

y = f(x) - 3

c)

y = f(x + 3)

d)

y = f(x) + 3

18.

The red graph shows the graph of y=f(x)

Identify the blue graph...

a)

y = f(-x)

b)

y = -f(x)

c)

y = f(x - 1)

d)

y = f(x) - 1

19.

Solve the following quadratic...

x² - 16 = 0

a)

x = -2, 8

b)

x = 2, -8

c)

x = 4, -4

d)

x = -1, -16

20.

Solve the following quadratic...

x² + 12x + 20 = 0

a)

x = 5, 4

b)

x = 2, 10

c)

x = -5, -4

d)

x = -2, -10

21.

What are the solutions to
v² + 6v + 5 = 0

a)

(1,0) and (0,0)

b)

(5, 0) and (-7, 0)

c)

(-5, 0) and (-1, 0)

d)

(6,0) and (0,0)

22.

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

23.

Find the zeros of the following quadratic function.

$f\left(x\right)\ =\ x^2\ -\ x\ -30$

a)

{x = -5, 6}

b)

{x = -6, 5}

c)

{x = -3, 10}

d)

{x = -10, 3}

24.

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

25.

$x^2+5x\ +8\ =0$

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

a)

$\frac{-5\pm\sqrt{57}}{2}$

b)

$\frac{5\pm\sqrt{57}}{2}$

c)

$\frac{-5\pm i\sqrt{7}}{2}$

d)

$\frac{5\pm i\sqrt{7}}{2}$

26.

$x^2-6x\ +12\ =0$

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

a)

$3\pm i\sqrt{3}$

b)

$3\pm\ \sqrt{3}$

c)

$\frac{6\pm\sqrt{-12}}{2}$

d)

$3\pm i$

27.

Convert to vertex form:

y = x² - 14x + 36

a)

y = (x + 7)² + 13

b)

y = (x - 7)² - 13

c)

y = (x - 7)² + 13

d)

y = (x + 7)² - 13

28.

What transformations have occurred in the function: $f\left(x\right)=-3\left(x-1\right)^2+6$

a)

Reflection across the x-axis; Vertical stretch of 3; Right 1; Up 6

b)

Horizontal compression of 3; Left 1; Down 6

c)

Horizontal stretch of 1; Reflection across the x-axis; Up 6

d)

Reflection across the x-axis; Vertical stretch of 3; Left 1; Up 6

29.

Which graph has factors of (x+1) and (x-3) ?

a)

b)

c)

d)

30.

Given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

31.

What is vertex of the quadratic function x²+4x-21?

a)

(4, -21)

b)

(-2,-25)

c)

(2, -21)

d)

(4, -25)

32.

What are the zeros of x²+9x+14

a)

2, 7

b)

-2, -7

c)

2, -7

d)

-2, 7

33.

Select the transformations of the following equation

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

(select all that apply)

a)

vertical compression

b)

Reflects across x-axis

c)

Shifts right 2 units

d)

Shifts left 2 units

34.

What are the increasing and decreasing intervals for the function: $g\left(x\right)=-2\left(x-3\right)^2+1$ ?

a)

Increasing: (−∞, 3)

Decreasing: (3, ∞)

b)

Increasing: (−∞, 1)

Decreasing: (1, ∞)

c)

Increasing: (2, ∞)

Decreasing: (-∞, 2)

d)

Increasing: (1, ∞)

Decreasing: (-∞, 1)

35.

How many real and imaginary solutions does this graph have?

a)

one real solution

no imaginary solutions

b)

two real solutions

c)

two imaginary solutions

d)

one real solution

one imaginary solution

36.

How many real and imaginary solutions does the quadratic have?

a)

Two imaginary solutions

b)

One real solution

One imaginary solution

c)

Two real solutions

d)

One real solution

No imaginary solutions

37.

What is the domain and range in this graph?

a)

D: (-∞, ∞)

R: (-1, ∞)

b)

D: (-4, 2)

R: (-1, ∞)

c)

D: (-∞, ∞)

R: (-∞, ∞)

d)

D: (-4, 2)

R: (-2.5, 2.5)

38.

Even or Odd degree?

a)

even

b)

odd

39.

How many real zeros does the function have?

a)

None

b)

2

c)

3

d)

4

40.

Which root has a multiplicity of 2?

a)

-1

b)

2

c)

4

d)

-4

41.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

42.

Determine the end behavior of the graph.

a)

As x→ -∞, y→ -∞
As x→ +∞, y→ +∞

b)

As x→ -∞, y→ -∞
As x→ +∞, y→ -∞

c)

As x→ -∞, y→ +∞
As x→ +∞, y→ +∞

d)

As x→ -∞, y→ +∞
As x→ +∞, y→ -∞

43.

a)

y = ^_(x + 2)(x - 1)²

b)

y = -(x - 2)(x + 1)²

c)

y = (x - 2)(x + 1)²

d)

y = -x³

44.

Identify the zeros

a)

x=2, x=6, x=-4

b)

(x+2)(x+6)(x-4)

c)

(x-2)(x-6)(x+4)

d)

x=-2, x=-6, x=4

45.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

a)

±1, ±8

b)

±1, ±2, ±4, ±8

c)

±1, ±2, ±4

d)

1, 2, 4, 8

46.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

a)

±1, ±7, ±1/3, ±7/3

b)

±1, 7

c)

±1, ±3, ±7, ±7/3

d)

±1, ±3, ±7, ±1/3, ±7/3

47.

10n²+100n+250

a)

10(n+5)²

b)

10(n-5)²

c)

10(n+5)(n-5)

d)

(5n+10)²

48.

Write 4x³+2x²-6x in factored form.

a)

2x(2x-3)(x+1)

b)

4x(2x+3)(x-1)

c)

2x(2x+3)(x-1)

d)

4x(2x-3)(x+1)

49.

Divide 3x^2 + 7x + 2 by x + 2.

a)

3x + 3

b)

3x - 1

c)

3x + 1

d)

3x - 3

50.

Find all factors of the polynomial x⁴ - 12x³ + 49x² - 78x + 40 by long division.

a)

(x-1)(x-2)(x-4)(x-5)

b)

(x+1)(x-2)(x-4)(x-5)

c)

(x-1)(x-2)(x+4)(x-5)

d)

(x-1)(x-2)(x-4)(x+5)

51.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

52.

Identify the missing term to complete the solution.

a)

4

b)

-4

c)

5

d)

-5

53.

Use the remainder theorem to find the value of p(c):

p(x) = 4x³ + 3x + 38, c = -2.

a)

p(-2) = 0 so

4x³ + 3x + 38 =

(x + 2)(4x³ - 8x + 19)

b)

p(-2) = 0 so

4x³ + 3x + 38 =

(x - 2)(4x³ - 8x + 19)

c)

p(-2) = 48

d)

p(-2) = 60

54.

Find the following using the Remainder Theorem for:

$f(x)=2x^4+6x^3-5x^2-60$

$f\left(-1\right)$

55.

Find the y intercept for $\frac{x^2-5x+6}{x^2-4x+3}$

a)

(0, 1) and (0, 3)

b)

(0, 2)

c)

(0, 3)

d)

(0, 6)

56.

What is the equation for the horizontal asymptote?

a)

y=1

b)

y=2

c)

x=1

d)

x=2

57.

What is the vertical asymptote?

a)

y=6

b)

y=-6

c)

x=2

d)

x=-2

58.

How is this function transformed from the parent function?

a)

Translated left and up

b)

Translated right and up

c)

Translated left and down

d)

Translated right and down

59.

What are the decreasing intervals of this function?

a)

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

b)

$\left(-\infty,3\right)U\left(3,\infty\right)$

c)

$\left(-\infty,3\right]$

d)

$\left(-\infty,3\right)\left(4,\infty\right)$

60.

Consider the function:

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

Does the function have any holes?

a)

yes, when $x=3$

b)

yes, when $x=0$

c)

yes, when $x=-2$

d)

The function does not have any holes.

61.

Consider the function

$y=\frac{3x-12}{x^2-2x-8}$

When $x=4,$ the function has a . . .

a)

Hole

b)

Vertical Asymptote

c)

Neither

62.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

63.

a)

y = 0

b)

y = 1/2

c)

y = 2

d)

None

64.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

65.

Solve for w:
$\frac{4}{w-2}=\frac{-1}{w+3}$

a)

2

b)

-2

c)

4

d)

-4

66.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

67.

Solve for x: $\frac{5}{x+2}=\frac{1}{x-4}$

a)

x = 5

b)

x = 4

c)

x = $\frac{11}{2}$

d)

x = -4

68.

Solve for x: $\frac{8}{x+3}=\frac{3}{x-5}$

a)

x = 49/5

b)

x = -5

c)

x = -49/5

d)

x = 5

1st Semester Algebra II Concepts Review

Total questions: 68

Worksheet time: 4hrs 58mins

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