Free Printable Algebra EOC Review #2

1.

Is the result rational or irrational? Explain.

a)

Rational; The sum of two rationals is always rational.

b)

Irrational; The sum of a rational and an irrational is always irrational.

c)

Rational; The product of two rationals is always rational.

d)

Irrational; The product of a nonzero rational and an irrational is always irrational.

2.

Solve:

3(y+5) ≥ 21

a)

y ≤ 2

b)

y ≥ 2

c)

y ≥ 12

d)

y ≤ 12

e)

y ≤ -2

3.

Match the graph to the inequality $9\le2m+2-3$

a)

A

b)

B

c)

C

d)

D

4.

Match the graph to the inequality $-5\left(x-3\right)+2x<6$

a)

A

b)

B

c)

C

d)

D

5.

Solve, and determine which numbers below are included in the solution.

4(5x + 2) ≤ 28

a)

1

b)

1.1

c)

0

d)

2

e)

0.5

6.

Solve, and determine which numbers below are included in the solution.

-8(x - 3) - 4x < 108

a)

-7

b)

-3

c)

-6

d)

-9

e)

0

7.

Which equation(s) describe the transformation of shifting two units right from the parent function?

a)

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

b)

$f\left(x\right)=\sqrt[]{x+2}$

c)

$f\left(x\right)=10^{\left(x-2\right)}$

d)

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

e)

$f\left(x\right)=x^{12}-2$

8.

The blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

9.

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

10.

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

11.

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

12.

What are the transformations of this functions compared to the parent function y = √(x)?

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch, and shifted right 5

c)

Reflected over the x-axis, vertical stretch, and shifted left 5

d)

Shifted right 5, shifted down 2

13.

What is the equation of the graph?

a)

$f\left(x\right)=4\sqrt[]{x}-5$

b)

$f\left(x\right)=\sqrt[]{x}+4$

c)

$f\left(x\right)=\sqrt[]{x-5}+4$

d)

$f\left(x\right)=\sqrt[]{x+4}+5$

e)

$f\left(x\right)=\sqrt[]{x+3}+5$

14.

Which equation represents this graph?

a)

f(x) = (x - 4)² - 3

b)

f(x) = -(x - 4)² + 3

c)

f(x) = (x - 4)² + 3

d)

f(x) = -(x + 4)² + 3

15.

$y=\sqrt{x}-2$

Which graph represents this transformed function

a)

b)

c)

d)

16.

$y=3\left|x\right|$

The dotted line is the parent function, the blue line is the new transformed function.

Which graph represents this transformed function?

a)

b)

c)

d)

17.

$y=-2\left|x\right|$

The dotted line is the parent function, the blue line is the new transformed function.

Which graph represents the transformed function?

a)

b)

c)

d)

18.

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

(a)

19.

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

a)

-42

b)

-26

c)

-18

d)

None of these

e)

23

20.

What is f( g(3) )?

a)

1/8

b)

8

c)

1/4

d)

1/2

e)

4

21.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of g( f(-2) ).

(a)

22.

(a)

23.

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

24.

Given f(x) = -3x+7 and g(x) = 2x² - 8, find f( g(x) ).

a)

f(g(x)) = -6x²+31

b)

f(g(x)) = -6x²+24

c)

f(g(x)) = 18x²- 84x + 6

d)

f(g(x))=9x²-42x-1

25.

What is the range of the graph?

a)

1 ≤ x ≤ 5

b)

1 < x < 5

c)

1 ≤ y ≤ 5

d)

1 < y < 5

26.

Given $g\left(x\right)=\frac{3}{4}x+10$ , find g(-12).

(a)

27.

Given f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find $f\left(x\right)+g\left(x\right)$

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

28.

f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find $f\left(x\right)-g\left(x\right)$

a)

x² + 8x + 1

b)

x² + 6x - 1

c)

5x² + 8x - 1

d)

x² + 8x -1

29.

$f\left(x\right)=2x+5$ and $g\left(x\right)=x-7$ Find $f\left(g\left(5\right)\right)$

(a)

30.

$f\left(x\right)=x-3$ and $g\left(x\right)=2x+6$ Find $g\left(f\left(-1\right)\right)$

(a)

31.

$f\left(x\right)=-x+4$ and $g\left(x\right)=5x-2$ Find $f\left(g\left(-3\right)\right)$

(a)

32.

If given the equation y = 3(x + 5)² - 4, select all the true statements.

a)

This parabola's y-intercept is (0, 71).

b)

The vertex is at (-5, -4)

c)

The axis of symmetry is x = 5.

d)

This parabola is downward facing.

e)

This parabola is stretched 3 times the steepness of the parent function.

33.

Select all the true statements about the parabola.

a)

The axis of symmetry is at

x = -5.

b)

The vertex is at

(5, -2).

c)

This parabola is stretched steeper than the parent function.

d)

This parabola is upward facing.

e)

This parabola has 2 zeros.

34.

Select the true statement about the parabola.

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

a)

This parabola has 1 zero.

b)

This parabola has a vertex at (1, 0)

c)

This parabola has 2 zeros, at (-1,0) and (1, 0).

d)

This parabola is more compressed than the parent.

e)

This parabola is downward facing.

35.

Select all the true statements about this parabola.

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

a)

This parabola has no x-intercepts.

b)

This parabola is more compressed than the parent.

c)

The axis of symmetry is at x = 3.

d)

The vertex is (2, 3).

e)

This parabola is upward facing.

36.

$y=4(x+2)^2-8$

Convert the equation from vertex form to standard form.

a)

$y=4x^2+16x+8$

b)

$y=4x^2+16x+16$

c)

$y=16x^2+64x-8$

d)

$y=16x^2+256x+8$

37.

Which of the following shows
f(x) = x² + 12x - 2
written in vertex form?

a)

f(x) = (x + 6)² + 142

b)

f(x) = (x + 6)² - 34

c)

f(x) = (x + 6)² - 38

d)

f(x) = (x + 6)² + 34

38.

Which of the following equations has 2 solutions?

a)

f(x) = x² + 6x - 2

b)

f(x) = (x - 1)² + 2

c)

f(x) = - (x - 1)² + 2

d)

f(x) = x² + 12x + 36

e)

f(x) = - (x - 1)² - 2

39.

Which of the following shows
f(x) = x² - 8x + 1
written in vertex form?

a)

f(x) = (x - 4)² - 15

b)

f(x) = (x - 4)² + 17

c)

f(x) = (x - 4)² - 17

d)

f(x) = (x - 4)² + 65

40.

Which function is equivalent to
y = x² - 6x + 10?

a)

y = (x + 3)² - 1

b)

y = (x - 3)² + 1

c)

y = (x + 6)² - 10

d)

y = (x - 6)² + 10

41.

Convert the equation y= x²+ 4x + 11 into vertex form.

a)

y = (x + 2)² - 4

b)

y = (x + 2)² + 7

c)

y = (x + 2)²

d)

y = (x - 2)² - 7

42.

Select all the true statements about this parabola.

a)

In vertex form: $f\left(x\right)=\left(x-4\right)^2+4$

b)

In factored form: $f\left(x\right)=\left(x-2\right)\left(x-6\right)$

c)

This function's minimum is 2.

d)

This function's y-intercept is (0, 12)

e)

This function's leading coefficient is greater than 1.

43.

What's the axis of symmetry?

y = 3x²- 6x + 4

a)

x = 1

b)

x = -6

c)

x = 2

d)

x = -1

44.

Select the true statements about the parabola.

f(x) = -3x² +7x - 2

a)

This function is upward facing.

b)

The y-intercept is (0, -2).

c)

This function is stretched steeper than the parent.

d)

This function's y-intercept is at (0, -3).

e)

This function's axis of symmetry is at x = -7.

45.

Select any of the following coordinates that are roots of this function.

a)

(0, 0)

b)

(2, 4)

c)

(0, 4)

d)

(4, 0)

e)

(1, 3)

46.

Factor x² + 4x - 21

a)

(x + 7)(x - 3)

b)

(x - 7)(x + 3)

c)

(x - 7)(x - 3)

d)

(x + 7)(x + 3)

e)

prime

47.

Solve
x² + 9x + 20 = 0

a)

x = -2, x = -10

b)

x = -3, x = -4

c)

x = -4, x = -5

d)

x = -4, x = -6

48.

Factor:

$x^2-10x+3$

a)

(x + 7)(x - 3)

b)

(x + 1)(x - 3)

c)

(x + 3)(x - 1)

d)

(x + 10)(x - 7)

e)

prime

49.

What is the equation of the line?

a)

$y=-\frac{3}{2}x-5$

b)

$y=\frac{2}{3}x+5$

c)

$y=\frac{3}{2}x+5$

d)

$y=-\frac{2}{3}x+5$

e)

$y=-\frac{3}{2}x+5$

50.

Which of the following relations represents y as a function of x?
I. {(1, 4), (2, 5), (3, 6)}
II. {(1, 4), (2, 4), (3, 4)}
III. {(1, 4), (2, 4), (1, 3)}
IV. {(1, 4), (1, 2), (1, 3)}

a)

I, II, and III only

b)

II and IV only

c)

III and IV only

d)

I and II only

Algebra EOC Review #2

Total questions: 50

Worksheet time: 2hrs 6mins

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