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WorksheetsPre-Calculus 12/17 - 12/21
Total questions: 135
Worksheet time: 33hrs 4mins
Name
Class
Date
1.
What do you do to the b value to correctly complete the square?
a)
square it
b)
divide it by 2 and square the result
c)
divide it by 2 and take the square root of the result
d)
divide it by 2 only
2.
Complete the square for
x2 + 12x + ____
x2 + 12x + ____
a)
x2 + 12x + 144
b)
x2 + 12x + 36
c)
x2 + 12x - 36
d)
x2 + +12x - 144
3.
Complete the square.
x2 + 6x + ____
x2 + 6x + ____
a)
x2 + 6x + 9
b)
x2 + 6x - 36
c)
x2 + 6x + 36
d)
x2 + 6x - 9
4.
Complete the square.
x2 + 14x + ____
x2 + 14x + ____
a)
x2 + 14x - 196
b)
x2 + 14x + 49
c)
x2 + 14x - 49
d)
x2 + 14x + 196
5.
What is the vertex?
a)
(2, 4)
b)
(3, -1)
c)
(0, 8)
d)
(4, 2)
6.
If the blue is f(x)=x2, the red must be
a)
g(x)=(x + 3)2
b)
g(x)=(x - 3)2
c)
g(x)=x2 + 3
d)
g(x)=x2 - 2
7.
What are the transformations from the parent function y = x2?
y=(x - 2)3 + 4
y=(x - 2)3 + 4
a)
shift right 2 shift up 4
b)
shift left 2 shift up 4
c)
shift right 2 shift down 4
d)
shift left 2 shift up 4
8.
Match the equation to its description.
a)
Right 2 and up 2
b)
Left 2 and up 2
c)
Right 2 and down 2
d)
Left 2 and down 2
9.
Identify the vertex and whether the graph opens up or down.
a)
(-1, 4); opens up
b)
(-1, 4); opens down
c)
(1, 4); opens up
d)
(1, 4); opens down
10.
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
11.
Find the Vertical Asymptotes
a)
x= 0, -2
b)
x= 2
c)
x= -3, 2
d)
x = -3,1
12.
What is the Vertical Asymptotes?
a)
x= -5
b)
x= 5
c)
x= 6
d)
x= -6
13.
Which asymptote(s) are determined by looking at the denominator?
a)
vertical
b)
horizontal
c)
slant
d)
none
14.
Find the Domain for the function : (2x2-4x)/(x2-2x-3)
a)
all real numbers except 3 and -1
b)
all real numbers except 3
c)
all real numbers except -1
d)
all real numbers except -3
15.
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)
16.
f(x) = {(3, 7), (4, -2), (5, -1), (8, 7)}
Is f-1(x) a function?
Is f-1(x) a function?
a)
Yes
b)
No
c)
No way to tell
17.
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
18.
a)
9 - √17
b)
4
c)
2
d)
√8
19.
What does it mean to find the inverse of a function?
a)
the x's and y's are switched
b)
the x's and y's are divided by 2
c)
the x's and y's are made negative
d)
the x's and y's are the same
20.
When finding the inverse of a relation,
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?
a)
solve for y
b)
replace y with f-1(x)
c)
solve for x
d)
find the greatest common factor
21.
Are these the graphs of two inverse functions?
a)
Yes
b)
No
c)
No way to tell
22.
Find the inverse of f(x) = 5/11x +10
a)
f-1(x) = 11/5x - 22
b)
f-1(x) = 5/11x - 22
c)
f-1(x) = 11/5x - 20
d)
None of the above
23.
What is the domain of this function?
a)
(0, ∞)
b)
[1, ∞)
c)
[1, 5]
d)
[2, ∞)
24.
f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))
g(x) = x - 2
Find f(g(5))
a)
19
b)
23
c)
-10
d)
None of these.
25.
If f(x) = 3x-1 and g(x) = x2+2,
what is (f ° g)(x) ?
a)
3x2 +5
b)
x2 +1
c)
3x2 +1
d)
3x2 +6
26.
Is point A on this graph a maximum or minimum?
a)
Maximum
b)
Minimum
27.
At what point is the minimum of this graph?
a)
(-1, 3)
b)
(3, -1)
c)
(0,3)
d)
(5,0)
28.
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
29.
Find the distance between the two points:
(1, -1) (-2, 3)
(1, -1) (-2, 3)
a)
√ 25
b)
√ 3
c)
5
d)
√ 29
30.
Find the midpoint between the points:
(4, -4) (4, 8)
(4, -4) (4, 8)
a)
(4,2)
b)
(0,-6)
c)
(0, -2)
d)
(4, -6)
31.
Write the equation of the line (in point slope form) given a slope of -2 and containing the point (3, -1)
a)
y - 1 = -2 (x - 3)
b)
y = -2x + 5
c)
y + 1 = -2 (x - 3)
d)
y + 2x = 5
32.
If the equation of a graph is y = x2 + 4, what kind of graph does it create?
a)
Straight Line
b)
Circle
c)
Parabola
d)
Point
33.
What is the slope of 4x + 6y = 36?
a)
m = 4
b)
m = -3/2
c)
m = -2/3
d)
m = -4
34.
Determine if the lines are parallel, perpendicular, or neither.
y = -2x + 4
y = 2x - 3
y = -2x + 4
y = 2x - 3
a)
Parallel
b)
Perpendicular
c)
Neither
35.
Factor completely:
10x2 + 15x-5
10x2 + 15x-5
a)
25(10x3+45x-15)
b)
5(2x3 + 3x2-x)
c)
x(10x3+15x-5)
d)
5(2x2+3x-1)
36.
Express the following in Interval Notation
-8 ≤ x < 8
-8 ≤ x < 8
a)
[-8, 8]
b)
[-8,8)
c)
(-8, 8]
d)
(-8, 8)
37.
Express the following interval in Set notation:
[3, 5]
[3, 5]
a)
3 ≤ x ≤ 5
b)
3 < x ≤ 5
c)
3 ≤ x < 5
d)
3 < x < 5
38.
Is the graph an even, odd, or neither function
f(x) = 4x3
f(x) = 4x3
a)
Even
b)
Odd
c)
Neither
39.
Is the graph an even, odd, or neither function
f(x) = x2 + 2
f(x) = x2 + 2
a)
Even
b)
Odd
c)
Neither
40.
Is the graph an even, odd, or neither function
f(x) = (x+4)2 - 1
f(x) = (x+4)2 - 1
a)
Even
b)
Odd
c)
Neither
41.
For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.
a)
D: {1, -3, -4,}
R: {0, 1, 2, -4}
R: {0, 1, 2, -4}
b)
D:{0, 1, 2, -4}
R:{1, -3, -4}
R:{1, -3, -4}
c)
D:{0, 1, 2, 3, 4}
R:{1, -3, -4}
R:{1, -3, -4}
42.
What is the range of this function?
a)
All real numbers.
b)
[2, infinity)
c)
[-2, infinity)
d)
[0, infinity)
43.
What is the interval of increase?
a)
(negative infinity, -2)
b)
(-2, infinity)
c)
(2, infinity)
d)
(negative infinity, 2)
44.
What is the interval of decrease?
a)
(negative infinity, -2)
b)
(-2, infinity)
c)
(2, infinity)
d)
(negative infinity, 2)
45.
Factor by grouping:
3x3-x2+6x-2
3x3-x2+6x-2
a)
(x2+2)(3x+1)
b)
(x2+2)(3x-1)
c)
(3x3+6x)(x2-2)
d)
none of the aboe
46.
Evaluate f(x)=-2x+13 for f(10)
a)
-7
b)
1
c)
-8
d)
7
47.
What is the value of f(0)?
a)
-2
b)
2
c)
4
d)
0
48.
Which graph does NOT pass the vertical line test?
a)
Graph 1
b)
Graph 2
c)
Graph 3
d)
Graph 4
49.
Is this mapping a function or not a function?
a)
Function
b)
Not a Function
50.
Is the relation a function? Why.
a)
Yes, because the x-value 11 has two y-values pair with it.
b)
Yes, because each x-value has only one y-value paired with it.
c)
No, because the x-value 11 has two y-values pair with it.
d)
No, because each x-value has only one y-value paired with it.
51.
What is m(-3) if:
a)
-3
b)
0.5
c)
3
d)
-3.5
52.
Which piecewise function corresponds to this graph? (Take your time)
a)
f(x) = { x if x < 4; -x+1 if x ≥ 4
b)
f(x) = { x if x ≤ 4; -x+1 if x > 4
c)
f(x) = { -x+1 if x < 4; x if x ≥ 4
d)
f(x) = { -x+1 if x ≤ 4; x if x > 4
53.
When f(x) = 9-3x and g(x) = 5x-7 , find f(x)+g(x).
a)
14x-10
b)
-8x+2
c)
2x+2
d)
2x-2
54.
When f(x) = x2+9 and g(x) = x-9, find f(x)-g(x).
a)
x2+x+9
b)
x2-x+9
c)
x2-x
d)
x2-x+18
55.
When f(x) = 4x+8 and
g(x) = x+3, find
f(x) * g(x).
g(x) = x+3, find
f(x) * g(x).
a)
4x2+24
b)
4x2+20x+24
c)
4x2+12x+24
d)
4x2+4x+24
56.
When 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
57.
f(x)=x+3
g(x)=x-2
Find (g/f)(x)
g(x)=x-2
Find (g/f)(x)
a)
(x+3)/(x-2)
b)
(x-2)/(x+3)
c)
-2/3
d)
3/2
58.
f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))
g(x) = x - 2
Find f(g(5))
a)
19
b)
23
c)
-10
d)
None of these.
59.
f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))
g(x) = x - 2
Find f(g(0))
a)
16
b)
4
c)
-4
d)
None of these.
60.
p(x) = 3x + 4
q(x) = 2x2
Find q(p(-2))
q(x) = 2x2
Find q(p(-2))
a)
8
b)
-8
c)
28
d)
None of these.
61.
Given
f(x) = 3x2 + 7x and g(x) = 2x2 - x - 1, find (f + g)(x).
f(x) = 3x2 + 7x and g(x) = 2x2 - x - 1, find (f + g)(x).
a)
11x2 - 1
b)
5x4 + 6x2 - 1
c)
5x2 + 6x - 1
d)
5x2 + 8x - 1
62.
f(x)=x2-1
g(x)=x-1
Find (f/g)(10)
a)
9
b)
11
c)
90
d)
110
63.
8r3 + 16r2
a)
4r2(2r + 4)
b)
8r2(r + 2)
c)
8(r3 + r2)
d)
4(r3 + 2r2)
64.
Factor
n2 + 5n - 6
n2 + 5n - 6
a)
(n - 2)(n - 3)
b)
(n - 1)(n + 6)
c)
(n + 1)(n - 6)
d)
(n + 2)(n - 3)
65.
Factor:
x2 - 9
x2 - 9
a)
(x + 3)(x - 3)
b)
(x + 3)2
c)
(x - 3)2
d)
(x+3)(x+3)
66.
Factor completely: 3x² - 7x + 2
a)
(x - 1) (3x + 2)
b)
(x - 2) (3x -1)
c)
(x - 1) (3x - 2)
d)
(x + 2) (3x + 1)
67.
Factorly Completely: 2x² - 7x + 6
a)
(x -1)(2x - 6)
b)
(x - 3) (2x - 2)
c)
(x - 2) (2x - 3)
d)
(x - 6) (2x - 1)
68.
Factor Completely: 4x² - 20x + 25
a)
(4x - 25) (x -1)
b)
(2x + 5) (2x - 5)
c)
(2x - 5)²
d)
(4x - 5) (x - 5)
69.
Factor x3 + 2x2 - 49x - 98
a)
(x2 - 49) (x + 2)
b)
(x2 - 49) (x + 2) (x + 2)
c)
(x + 7) (x - 7) (x + 2)
70.
Factor p3 - 3p2 - 16p + 48
a)
p2 ( p - 3) (p - 3)
b)
(p2 - 16) (p - 3)
c)
(p + 4) (p - 4) (p - 3)
71.
30x3+15x2-18x-9
a)
(5x2-3)(6x+1)
b)
(5x2-3)(6x+3)
c)
3(5x2+3)(2x-1)
d)
3(5x2-3)(2x+1)
72.
a)
Function
b)
Not a Function
73.
a)
Function
b)
Not a Function
74.
If h(a) = 3 - 2a2
Find h(-3).
Find h(-3).
a)
33
b)
21
c)
39
d)
-15
75.
Is this graph a function or not a function?
a)
Function
b)
Not a Function
76.
Is this set of ordered pairs a function or not a function?
a)
Function
b)
Not a function
77.
Is this set of ordered pairs a function or not a function?
a)
Function
b)
Not a Function
78.
Factor: 8x³ - 64
a)
(2x + 4)(4x² - 8x + 16)
b)
(2x - 4)(4x² + 8x + 16)
c)
(2x - 4)(x² + 8x + 16)
d)
(2x + 4)(x² - 8x + 16)
79.
Factor: 27x³ + 125
a)
(3x + 5)(x² - 15x + 25)
b)
(3x - 5)(x² + 15x + 25)
c)
(3x - 5)(9x² + 15x + 25)
d)
(3x + 5)(9x² - 15x + 25)
80.
Compare in words, the graph of y = -7(x - 2)³ + 6 to its parent function.
a)
Reflection over the x -axis, Vert. shift up 6 units, Horiz. shift right 2 units, vertical stretch by a factor of 7
b)
Reflection over the x -axis, Vert. shift down 2 units, Horiz. shift right 6 units, vertical shrink by a factor of 7
81.
If f(x) = x² + 2x - 4, find [f(x + h) - f(x)] / h
a)
2x + 2
b)
2x + h + 2
82.
a)
10x11y9
b)
10x3/y3
c)
10y3/x3
d)
10x11/y9
83.
Factor x2 -16x + 48
a)
(x - 12)(x - 4)
b)
(x + 6)(x - 8)
c)
(x + 12)(x - 4)
d)
(x -16)(x - 3)
84.
What is f(-2)?
a)
4
b)
-1
c)
1
d)
DNE
85.
Complete the square.
x2 + 6x + ____
x2 + 6x + ____
a)
x2 + 6x + 9
b)
x2 + 6x - 36
c)
x2 + 6x + 36
d)
x2 + 6x - 9
86.
Convert to vertex form.
a)
y=2(x+3)2 - 9
b)
y=2(x-3)2 - 9
c)
y=2(x+6)2 - 9
d)
y=2(x-6)2 - 9
87.
a)
b)
c)
d)
e)
88.
a)
b)
c)
d)
e)
89.
a)
b)
c)
d)
e)
90.
a)
b)
c)
d)
e)
91.
a)
b)
c)
d)
e)
92.
Simplify:
a)
b)
c)
d)
e)
93.
Determine if the following equation is symmetric.
2x=3y2
2x=3y2
a)
Yes; y-axis
b)
Yes; x-axis
c)
Yes; y-axis, x-axis, and origin
d)
Not Symmetical
94.
Write the equation of the line (in point slope form) given a slope of -2 and containing the point (3, -1)
a)
y - 1 = -2 (x - 3)
b)
y = -2x + 5
c)
y + 1 = -2 (x - 3)
d)
y + 2x = 5
95.
Write the equation of the line parallel to x - y = -4 containing the point (-5, 3) in slope intercept form.
a)
y - 3 = 1 (x +5 )
b)
y = x + 2
c)
y = -x - 2
d)
y = x + 8
96.
Write the equation of the circle in standard form given
(h, k) = (-2, 3)
r = 4
(h, k) = (-2, 3)
r = 4
a)
(x+2)2 + (y-3)2 = 4
b)
(x+2)2 + (y-3)2 = 16
c)
(x-2)2 + (y+3)2 = 16
d)
(x+2)2 + (y+3)2 = 4
97.
Find the center and radius of the circle:
x2 + y2 - 2x + 4y - 4 = 0
x2 + y2 - 2x + 4y - 4 = 0
a)
Center: (1, -2); r = 4
b)
Center: (2, -4); r = 3
c)
Center: (2, -4); r = 2
d)
Center: (1, -2); r = 3
98.
Transform the equation of the circle from general form to standard form.
x2 + y2 - 8x + 6y = 0
x2 + y2 - 8x + 6y = 0
a)
(x + 4)2 + (y + 3)2 = 25
b)
(x - 4)2 + (y - 3)2 = 25
c)
(x - 4)2 + (y + 3)2 = 25
d)
(x - 4)2 + (y + 3)2 = 5
99.
What is the domain of the graph?
a)
1≤ x ≤ 4
b)
1 < x < 4
c)
1≤ y ≤ 4
d)
1 < y < 4
100.
What is the range of the graph?
a)
1 ≤ x ≤ 5
b)
1 < x < 5
c)
1 ≤ y ≤ 5
d)
1 < y < 5
101.
What is the domain of the graph?
a)
y≥1
b)
x ≥ 1
c)
All real numbers
d)
none of these
102.
What is the range of the graph?
a)
y≥1
b)
x≥1
c)
All real numbers
d)
none of these
103.
What is the domain of the graph?
a)
(-7,5)
b)
[-3,1)
c)
(-3,1)
d)
[-7,5)
104.
What is the Range of this linear function?
a)
-6 ≤ y ≤ 6
b)
0 ≤ y ≤ 6
c)
No Solution
d)
4 ≤ y ≤ 3
105.
What is the range?
a)
[-7,6)
b)
(-7,6)
c)
(-8,2)
d)
[-8,2]
106.
Evaluate f(-5)
a)
0
b)
2
c)
5
d)
-4
107.
Find x if f(x) = 0.
a)
5
b)
-1
c)
-5
d)
-1 and -5
108.
Find x if f(x) = 6.
a)
0
b)
-2
c)
6
d)
-2 and 0
109.
What is g(7) if:
a)
-17
b)
-13
c)
13
d)
17
110.
Using the pictured graph, what is f(-3)?
a)
-3
b)
-1
c)
1
d)
3
111.
What is the DOMAIN of the function?
a)
(-∞, +∞)
b)
(-∞, 4]
c)
(-∞, 4)
d)
[0, 4]
112.
Simplify the expression
a)
6x / 20xy
b)
3 / 10y
c)
(6x+1) / (20xy)
d)
3 / 20xy
113.
Simplify the expression
a)
(2a + 4b) / 12b2
b)
(2a - 4b) / 12b2
c)
(a - b) / 6b2
d)
(a + 2b) / 6b2
114.
Simplify the expression
a)
(5x + 4y) / 9y
b)
(6y + 3x) / 3y
c)
(2y + x) / y
d)
(6y + 3x) / 9y
115.
Simplify the expression
a)
(19k2 -12k - 12) / 4k(5k-4)
b)
(19k2 - 24k) / 4k(5k-4)
c)
(19k) / 4(5k-4)
d)
(19k - 24) / 4(5k-4)
116.
Multiply and Simplify
a)
4(x+3)/(x+2),
b)
(x+2)/4(x+1)
c)
(x+2)/4(x+3),
d)
4(x+1)/(x+2),
117.
Multiply and Simplify
a)
(n-10)/8n+56
b)
(n-10)(n+7)/8n+56
c)
(n-10)/8
d)
(n+10)/8
118.
Divide and Simplify
a)
A
b)
B
c)
C
d)
D
119.
Simplify.
a)
(m+6)/(m-3)
b)
7/(m-3)
c)
7(m+6)
d)
(m-3)
120.
State domain restriction. What can x not be equal to?
a)
x≠-6
b)
x≠-6, 3
c)
x≠3
d)
x≠-18
121.
State domain restrictions. What can x not be equal to?
a)
x≠6,5
b)
x≠-6,5
c)
x≠-6,-5
d)
x≠6
122.
Simplify by cancelling
a)
1
b)
-1
c)
Can't be simplified
123.
Factor (GCF, Diff of sq, mult/add)
a)
1/6
b)
x+10/ 6x+60
c)
x+8/ 6x+60
d)
(x+10)(x+8)/ 6x+60
124.
Simplify.
a)
A
b)
B
c)
C
d)
D
125.
Divide the rational expressions.
a)
1/6
b)
x+10/ 6x+60
c)
x+8/ 6x+60
d)
(x+10)(x+8)/ 6x+60
126.
Simplify
a)
A.(x+7)/(x-4)
b)
B.-3/4
c)
C.(x+3)/(x+4)
d)
D.(x+3)/(x-4)
127.
Simplify
a)
A.4x³/(x+2)
b)
B.4x³/(x+10)
c)
C.2x³/(5x+1)
d)
D. 2x³/(x+5)
128.
Simplify
a)
(x-9)/(x+9)
b)
1/(x-9)
c)
(x+9)
d)
1/(x+9)
129.
Multiply and Simplify
a)
4(x+3)/(x+2),
b)
(x+2)/4(x+1)
c)
(x+2)/4(x+3),
d)
4(x+1)/(x+2),
130.
Multiply and Simplify
a)
5a-25/ (a-5)(a+9)
b)
5/(a+9)
c)
5a-25/ (a+9)
d)
1/(a+9)
131.
Multiply and Simplify
a)
(n-10)/8n+56
b)
(n-10)(n+7)/8n+56
c)
(n-10)/8
d)
(n+10)/8
132.
Multiply and Simplify
a)
2(x+8) / (x-2)
b)
(x-2)
c)
(x+4) / (x-6)
d)
(x-4) / (x+8)
133.
Divide and Simplify
a)
A
b)
B
c)
C
d)
D
134.
Simplify the expression
a)
(12n2 + 28n + 4) / (2n-5)(n+2)
b)
(12n2 - 28n + 4) / (2n-5)(n+2)
c)
(8n) / (3n + 3)
d)
(12n2 + 2n -3) / (2n-5)(n+2)
135.
Simplify the expression
a)
(19k2 -12k - 12) / 4k(5k-4)
b)
(19k2 - 24k) / 4k(5k-4)
c)
(19k) / 4(5k-4)
d)
(19k - 24) / 4(5k-4)
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