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Alg. 2 Final Exam Study

Total questions: 57

Worksheet time: 14hrs 15mins

Name
Class
Date
1.
Rewrite 34 = 81 in logarithmic form.
a)
log34 = 81
b)
log813 = 4
c)
log381 = 4
d)
log481 = 3
2.

Describe the end behavior of the function shown: y=log2(x+1)

a)
b)
c)
3.
Write logb(xy) as two logs
a)
logbx+logby
b)
logbx-logby
c)
logbx*logby
d)
logbx/logby
4.
a)

Parabola

b)

Circle

c)

Ellipse

d)

Hyperbola

5.
What is the vertex of the parabola: y=2(x-3)2+4
a)
(3,4)
b)
(-3,4)
c)
(3, -4)
d)
(-3,-4)
6.
Identify the vertex and whether the graph opens up or down.
a)
(5, 2); opens up
b)
(5, 2); opens down
c)
(-5, 2); opens up
d)
(-5, 2); opens down
7.
The focus is at (2,0) and the vertex is at (-4,0).  What is the equation of the parabola?
a)
y2 = 24(x+4)
b)
(y+4)2 = -12x
c)
x2 = 16(y+4)
d)
(x+4)2  = -20y
8.
Find the volume of a rectangular prism with length (x+2), width (x-4), and height (2x+1). (V=lwh)
a)
2x3-3x2-18x-8
b)
x2-2x-8
c)
2x3+5x2+18x-8y
9.
Find the volume of this prism
a)
-8x + 12
b)
5x² - 3x - 14
c)
4x³ - 10x² - 2x + 12
d)
5x - 5
10.
Factor completely 
16x2 - 16x - 12?
a)
A
4(2x - 2) (2x + 2)
b)
B
(2x - 3) (8x + 4)
c)
C
(8x - 12) (2x + 3)
d)
D
4(2x - 3) (2x + 1)
11.
Factor
x2 - 13x + 36
a)
A
(x + 9)(x + 4)
b)
B
(x - 9)(x - 4)
c)
C
(x + 9)(x - 4)
d)
D
(x - 9)(x + 4)
12.
Factor
3v2 - 4v - 7
a)
(3v-7)(v+1)
b)
3(v-7)(v-1)
c)
(3v+1)(v-9)
d)
(3v+1)(v-10)
13.
Divide: 

(4x2 - 24x + 35) / (2x - 5)
a)
2x - 7
b)
2x - 12
c)
2x + 12
d)
2x + 7
14.
Convert the equation y= x2-2x-5 into vertex form. 
a)
y= (x-1)2-6
b)
y= -(x-1)2-6
c)
y= (x+1)2-6
d)
y= -(x+6)2-1
15.
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
16.

What is the axis of symmetry in the function f(x) = (x-1)2 +2

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

17.

Identify the minimum and the domain of the function y = -2(x+1)2 + 4

a)

Max: 4, Domain: All Real Numbers

b)

Min: -4, Domain: All Real Numbers

c)

Max: 2, Domain: All real numbers when x is greater than 4

d)

Min: -2, Domain: All real numbers when x is less than 4

18.
Match the equation to its description.
a)
Stretched by 4 and up 4
b)
Compressed by 4 and up 4
c)
Stretched by 4 and left 4
d)
Compressed by 4 and left 4
19.
Match the equation to its description.
a)
Stretched by 4 and up 4
b)
Compressed by 4 and up 4
c)
Stretched by 4 and left 4
d)
Compressed by 4 and left 4
20.
Match the equation to its description.
a)
Reflected over x, right 2 and up 1
b)
Reflected over x, left 2 and up 1
c)
Reflected over x, right 2 and down 1
d)
Reflected over x, left 2 and down 1
21.
Which of the following is the correct equation for the given graph?
a)
f(x) = (x - 2)2 - 1
b)
f(x) = (x + 2)2 - 1
c)
f(x) = -(x + 2)2 - 1
d)
f(x) = -(x - 2)2 - 1
22.

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

a)
b)
c)
d)
23.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 2

d)

y = 4

24.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

25.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1/2

d)

y = 1

26.

State what type of variation the equation represents.

a)

Direct

b)

Inverse

c)

Joint

d)

None

27.

State what type of variation the equation represents.

a)

Direct

b)

Inverse

c)

Joint

d)

None

28.

State what type of variation the equation represents.

a)

Direct

b)

Inverse

c)

Joint

d)

None

29.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
30.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
31.
Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3
a)
reflected over x axis, stretched by 2, right 3, up 3
b)
reflected over x axis, stretched by 2, left 3 up 3.
c)
reflected over x axis, shrunk by 2, right 3, up 3
d)
reflected over the x axis, shrunk by 2, left 3, up 3
32.
What is the equation of the graph below?
a)
f(x) = I x + 2 I 
b)
f(x) = I x + 2 I +2
c)
f(x) = I x - 2 I +2
d)
f(x) = I x - 2 I 
33.

Write the equation for a graph that is vertically compressed by a factor of 2/5 and shifted right 6.

a)

y=6|x|-2/5

b)

y=2/5|x|+6

c)

y=2/5|x+6|

d)

y=2/5|x-6|

34.
Describe the transformations from the parent graph to f(x) = -3∣x + 5∣ - 7
a)
Down 7, Left 5, Stretch by 3, Flip
b)
Up 7, Right 5, Stretch by 3, Flip
c)
Down 7, Left 5, Compress by 3, Flip
d)
Up 7, Right 5, Compress by 3, Flip
35.
|v + 8| − 5 = 2 
a)
{-1,-15}
b)
{-1,-5}
c)
{-15,15}
d)
No Solution
36.
−2|−2r − 4| = -12
a)
{3,1}
b)
{-3,-1}
c)
{-3}
d)
No Solution
37.
Solve |2x –3| + 5 =10.
a)
-1, 1
b)
-1, 4
c)
-1, -4
d)
1, 4
38.

What is the equation for the graph?

a)

f(x) ≥|x-2|

b)

f(x) >|x-2|

c)

f(x) ≥|x+2|

d)

I don't know

39.

Which of the following could be the graph of f(x) > -2|x+2|+1

a)
b)
c)
d)
40.
Find the sum.
(3y2 + y3 - 5) + (4y2 -4y + 2y3 + 8)
a)
3y3 + 7y2 - 4y + 3
b)
4y2 + 3y3 - y + 3
c)
-y4 + 2y3 -y - 4
d)
4y3 + 3y2 -3y + 1
41.
Find the difference. 
(3- 2x + 2x2) - (4x -5 +3x2)
a)
x2 + 6x + 8
b)
2x2 + 5x - 7
c)
-x2 -6x + 8
d)
-2x2 + 11x - 4
42.
Find the difference.
(7p + 4p3 - 8) - (-3p2 + 2 - 9p)
a)
-3p2 + 4p3 -15 + 9
b)
3p3 + 4p2 - p + 3
c)
4p3 -3p2 +16p -10
d)
4p3 +3p2 + 16p + 10
43.
Find the product:
(x + 7)2
a)
x2 + 7x + 7x + 49
b)
x2 + 7x + 7
c)
7x2 + x + 7
d)
x2 + 14x + 49
44.
Multiply.
(b+3)(b2+2b+1)
a)
b3+6b2+6b+3
b)
b3+5b2+7b+3
c)
4b3+8b2+3b
d)
3b3+6b2+3b
45.
(2x3 + 5x2 + 9)
÷
(x + 3)
a)
2x2 - x + 3
b)
2x3 - x2 + 3x
c)
2x2 + 11x + 33 + 108/x+3
d)
2x2 - 5x + 12
46.
(3x3 + 5x - 1)
 ÷
(x + 1)
a)
3x3 - 3x2 + 8x - 9
b)
3x2 - 3x + 8 - 9/x+1
c)
3x2 + 3x + 8 + 7/x+1
d)
3x3 + 3x2 + 8x + 7
47.

Which expression is equivalent to the given?

a)
b)
c)
d)
48.
Rewrite each expression with a negative exponent.
1/124
a)
1/12-4
b)
124
c)
1/20,736
d)
12-4
49.
∛512 = ?
a)
≈177
b)
-8
c)
-8, 8
d)
8
50.
Solve           -4x2 = -36
a)
+, - 9
b)
+, - 3
c)
9
d)
3
51.
8
a)
W
b)
O
c)
R
d)
K
52.
a)
A
b)
B
c)
C
d)
D
53.
a)
A
b)
B
c)
C
d)
D
54.
a)
A
b)
B
c)
C
d)
D
55.
7n+10- 8 = 6
a)
-7.374
b)
-8.643
c)
-7.360
d)
-8.853
56.
log(x+6) = 1
a)
4
b)
4.222
c)
-5
d)
-9.550
57.
Change to Exponential Form:
log636 = 2
a)
26=36
b)
62=36
c)
362=6
d)
366=2

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