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Worksheets3/24 - Rational Functions and Parent Functions and factoring
Total questions: 75
Worksheet time: 6hrs 28mins
Name
Class
Date
1.
Name the parent function.
a)
square root
b)
quadratic
c)
cubic
d)
exponential
2.
a)
y=√x
b)
y=x2
c)
y=x3
d)
y=|x|
3.
f(x) = -√(x) - 2
a)
Reflect over x-axis
Down 2
Down 2
b)
Reflect over y-axis
Up 2
Up 2
c)
Reflect over x-axis
Up 2
Up 2
d)
Reflect over y-axis
Down 2
Down 2
4.
What is the equation of this graph?
a)
f(x) = (x + 2)2 - 3
b)
f(x) = (x - 2)2 - 3
c)
f(x) = |x + 2| - 3
d)
f(x) = |x - 2| - 3
5.
What is the equation of this graph?
a)
f(x) = -(x + 1)2 + 3
b)
f(x) = -(x - 1)2 + 3
c)
f(x) = -(x + 1)2 - 3
d)
f(x) = -(x + 1)2 - 3
6.
If the blue is f(x)=x2, then the red must be
a)
g(x)=x2-5
b)
g(x)=x2+5
c)
g(x)=(x-5)2
d)
g(x)=(x+5)2
7.
g(x)=f(x)-4
Describe the transformation to f(x) that results in g(x).
Describe the transformation to f(x) that results in g(x).
a)
f(x) has been translated down 4.
b)
f(x) has been translated up 4.
8.
g(x)=f(x-3)
Describe the transformation to f(x) that results in g(x).
Describe the transformation to f(x) that results in g(x).
a)
f(x) has been translated to the right 3.
b)
f(x) has been translated to the left 3.
9.
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
10.
Which equation below is a quadratic function translated left 4 units?
a)
y = x2 + 4
b)
y = (x + 4)2
c)
y = (x - 4)2
d)
y = 4x2
11.
a)
horizontal shift to the right 4 and vertical shift down 2
b)
horizontal shift to the left 4 and vertical shift up 2
c)
horizontal shift to the right 4 and vertical shift up 2
d)
horizontal shift to the left 4 and vertical shift down 2
12.
a)
horizontal shift to the left 2 and vertical stretch by a factor of 3
b)
horizontal shift to the right 2 and vertical stretch by a factor of 3
c)
horizontal shift to the right 2 and vertical compression by a factor of 3
d)
horizontal shift to the left 2 and vertical compression by a factor of 3
13.
What type of function is shown?
a)
cube root
b)
square root
c)
logarithm
d)
exponential
14.
Which parent function matches the graph?
a)
y = |x|
b)
y = ∛(x)
c)
y = x2
d)
y = a⋅bx
15.
Describe the effect on the vertex of the parabola y= x2-2 if the equation is changed to y=x2+4
a)
The vertex is translated upwards 6 units
b)
The vertex is translated downwards 6 units
c)
The vertex is translated upwards 4 units
d)
The vertex is translated downwards 4 units
16.
Describe the effect on the vertex of the parabola y= 100x2 if the equation is changed to y= -100x2
a)
The vertex is translated downwards 100 units
b)
The vertex is translated upwards 100 units
c)
The vertex does not change
d)
The vertex is flipped across the x-axis
17.
Let f(x)=√(x) and g(x)= -3√(x-2)+1. Describe g(x) in terms of f(x):
a)
flip over x axis, vertical stretch, right 2, up 1
b)
flip over y axis, vertical compression, left 2, up 1
c)
flip over x axis, vertical stretch, left 2, up 1
d)
flip over y axis, vertical compression, right 2, up 1
18.
Let f(x)=(x+1)2 and g(x)=f(x)+2. Describe the transformation applied to g(x)
a)
up 2
b)
right 1, up 2
c)
left 1, up 2
d)
down 2
19.
a)
Left 2, Down 2, Vertical Stretch
b)
Right 2; Up 1;
c)
Vertical Stretch; Right 2; Up 1
d)
Left 2; Down 2;
20.
a)
Left 2; Up 2
b)
Right 2; Down 2
c)
Left 2; Up 2; Reflection over x-axis
d)
Vertical stretch by factor of 3; Right 2; Down 2
21.
a)
Reflection over y-axis; Right 3; Up 1
b)
Right 3; Up 1
c)
Reflection over x-axis; Left 3; Up 1
d)
Reflection of x-axis; Right 3; Up 1
22.
a)
Right 4; Up 3
b)
Vertical Stretch by factor of 3; Horizontal Stretch by factor of 1/4
c)
Vertical Stretch by factor of 4; Horizontal Stretch by factor of 3
d)
Vertical Compression by factor of 3; Horizontal compression by factor of 4
23.
a)
Left 2; Down 1
b)
Reflection over x-axis; Left 2; Up 1
c)
Reflection over x-axis; Left 2; Down 1
d)
Reflection over y-axis; Right 2; Down 1
24.
a)
Vertical Stretch by factor of 3; Reflection over x-axis; Left 3
b)
Horizontal Compression by factor of 3;Reflection over y-axis; Left 3
c)
Vertical Stretch by 3; Reflection over y-axis; Left 3
d)
Reflection over x-axis; Left 3
25.
a)
Quadratic
b)
Cubic
c)
Cube Root
d)
Square Root
26.
a)
Absolute Value
b)
Quadratic
c)
Cubic
d)
Linear
27.
a)
Cube Root
b)
Square Root
c)
Quadratic Root
d)
Cubic
28.
a)
Square Root
b)
Quadratic
c)
Cube Root
d)
Cubic
29.
a)
Cubic
b)
Quadratic
c)
Absolute Value
d)
Square Root
30.
a)
Square Root
b)
Quadratic
c)
Absolute Value
d)
Linear
31.
a)
f(x)=x2 + 2
b)
f(x) = (x-2)2 + 1
c)
f(x)= (x+2)2 - 1
d)
f(x)= (x+2)2 + 1
32.
a)
f(x)=3∣x−2∣−2
b)
f(x)=1/3∣x+2∣−2
c)
f(x)=3∣x+2∣−2
d)
f(x) = 1/3∣x−2∣+2
33.
a)
A).
b)
B).
c)
C).
d)
D.)
34.
a)
f(x) = −(x−2)3−1
b)
f(x) = −(x+2)3−1
c)
f(x) = −(x−2)3 + 1
d)
f(x) = −(x+2)3 + 1
35.
a)
f(x) = −3(x+3)2
b)
f(x) = −3x2 + 3
c)
f(x) = −(3x−3)2
d)
f(x) = (−3x)2 − 3
36.
Which equation below is a quadratic function translated up 5 units?
a)
y = x2 + 5
b)
y = (x + 5)2
c)
y = 5x2
d)
y = -x2 - 5
37.
Which equation is a quadratic function reflected over the x-axis and shifted up 2.
a)
y = x2 + 2
b)
y = -x2 + 2
c)
y = x2 - 2
d)
y = -(x + 2)2
38.
Tell how the function transformed from y =|x|
y = -2|x|
y = -2|x|
a)
Translated left 2 units
b)
Reflected over x-axis
c)
Stretched vertically and reflected over x-axis
d)
Compressed vertically and reflected over the x-axis
39.
a)
y = Ix + 2I - 1
b)
y = -Ix + 2I - 1
c)
y = -Ix - 2I - 1
d)
y = -Ix + 1I - 2
40.
What are the transformations to the graph compared to the parent function?
a)
Shifted right 2, shifted up 3, and reflected over the y-axis
b)
Shifted left 2, shifted up 3, and reflected over the y-axis
c)
Shifted left 2, shifted up 3, and reflected over the x-axis
d)
Shifted right 2, shifted up 3, and reflected over the x-axis
41.
Match the equation with the graph:
a)
y = (x - 2)2 + 4
b)
y = -(x - 4)2 + 2
c)
y = -(x - 2)2 + 4
d)
y = -(x + 2)2 + 4
42.
Which equation below is a quadratic function translated left 4 units?
a)
y = x2 + 4
b)
y = (x + 4)2
c)
y = (x - 4)2
d)
y = 4x2
43.
Which equation is an absolute value graph shifted right 5 units?
a)
y = |x - 5|
b)
y = |x + 5|
c)
y = |x| + 5
d)
y = -5|x|
44.
A vertical asymptote is found by setting the _________= to zero and solving for x
a)
Numerator
b)
Denominator
c)
Right side
d)
Left side
45.
Find the domain of the rational function
f(x) = x/(x2-25)
a)
( -∞ , -5) U (5, ∞)
b)
(-∞, -5) U (-5, 5) U (5, ∞)
c)
(-∞, 5) U (5, ∞)
d)
(-∞, 25) U (25, ∞)
46.
Find the x-intercept of the function f(x) = (x - 7) / x
a)
(0, 0)
b)
(0, -7)
c)
(7, 0)
d)
there is no x- intercept
47.
Determine the x-coordinate of the hole on the graph of
f(x)= (x2-2x + 1)/(x2+2x - 3)
f(x)= (x2-2x + 1)/(x2+2x - 3)
a)
-1
b)
3
c)
1
d)
-3
48.
What are the asymptotes of the following function:
y = x / (2x - 6)
y = x / (2x - 6)
a)
y = 1/2, x = 3
b)
y = 2, x = 6
c)
y = 1/2, x = 6
d)
y = 2, x = 3
49.
Factor out the GCF:
12x + 6
12x + 6
a)
6(2x + 1)
b)
3(4x + 2)
c)
6x(2x + 1)
d)
2(6x + 3)
50.
Factor:
x² - 5x - 14
x² - 5x - 14
a)
(x - 2)(x + 3)
b)
(x - 2)(x + 7)
c)
(x + 2)(x - 7)
d)
(x - 2)(x - 3)
51.
Factor:
2x² + 13x + 15
2x² + 13x + 15
a)
(2x + 1)(x + 15)
b)
(x + 3)(x + 5)
c)
(2x - 3)(x - 5)
d)
(2x + 3)(x + 5)
52.
Factor:
2x² -15x + 27
2x² -15x + 27
a)
(2x - 9)(x - 3)
b)
(2x + 9)(x + 3)
c)
(2x - 5)(x - 3)
d)
(x - 9)(x - 3)
53.
Factor:
8x² + 22x + 5
8x² + 22x + 5
a)
(x + 1)(2x + 5)
b)
(8x + 1)(x + 5)
c)
(4x + 1)(2x + 5)
d)
(4x - 1)(2x - 5)
54.
Factor:
x² + 21x + 108
x² + 21x + 108
a)
(x + 9)(x + 12)
b)
(x + 3)(x + 27)
c)
(x + 2)(x + 54)
d)
(x + 4)(x + 27)
55.
Factor:
10x² + 9x - 7
10x² + 9x - 7
a)
(5x + 10)(2x - 7)
b)
(10x + 2)(x - 3)
c)
(5x + 3)(2x + 1)
d)
(5x + 7)(2x - 1)
56.
Factor:
2x² + 11x + 14
2x² + 11x + 14
a)
(x + 7)(2x + 2)
b)
(x + 2)(2x + 7)
c)
(x + 14)(2x + 1)
d)
(x + 1)(2x + 14)
57.
Factor:
12x² + 11x + 2
12x² + 11x + 2
a)
(12x + 1)(x + 2)
b)
(3x + 1)(4x + 2)
c)
(3x + 2)(4x + 1)
d)
(12x + 2)(x + 1)
58.
Factor out the GCF:
10x³ - 15x
10x³ - 15x
a)
x(10x² - 15)
b)
5x(2x² - 3)
c)
5(2x³ - 3x)
d)
5x²(10x - 3)
59.
Factor
x2 + 9x - 36
x2 + 9x - 36
a)
(x + 12)(x - 3)
b)
(x + 9)(x - 4)
c)
(x - 12)(x + 3)
d)
(x - 9)(x - 4)
60.
Factor
n2 + 16n + 63
n2 + 16n + 63
a)
(n-7)(n+4)
b)
(n+7)(n-9)
c)
(n-3)(n-10)
d)
(n+7)(n+9)
61.
Factor
k2 - 2k - 24
k2 - 2k - 24
a)
(k+4)(k-6)
b)
(k+4)(k+6)
c)
(k+6)(k-1)
d)
(k-4)(k+6)
62.
Factor
x2 - 5x - 36
x2 - 5x - 36
a)
(x - 4)(x + 9)
b)
(x - 6)(x + 6)
c)
(x + 4)(x - 9)
d)
(x -12)(x + 3)
63.
Factor
3v2 - 4v - 7
3v2 - 4v - 7
a)
(3v-7)(v+1)
b)
3(v-7)(v-1)
c)
(3v+1)(v-9)
d)
(3v+1)(v-10)
64.
Factor
3a2 + 4a + 1
3a2 + 4a + 1
a)
(7a-10)(a-8)
b)
Not factorable
c)
(3a+1)(a+1)
d)
(3a-1)(a-1)
65.
Factor:
4h² - 17h + 4
4h² - 17h + 4
a)
(2h - 2)²
b)
4(h + 4)(h + 1)
c)
(2h - 2)(2h + 2)
d)
(h - 4)(4h - 1)
66.
Factor:
2m² + 3m - 9
2m² + 3m - 9
a)
2(m + 3)(m - 3)
b)
(2m - 3)²
c)
(m + 3)(2m - 3)
d)
(2m + 3)(m - 3)
67.
The area of a rectangle is (x2 + 17x+42) ft2. If its width is (x + 3) ft. What is its length?
a)
(x + 17) ft
b)
(x + 14) ft
c)
(x - 14) ft
d)
(x - 17) ft
68.
A classroom has an area of 3x2 + 7x + 2. If the length of the classroom is (3x + 1), what is the width of the classroom?
a)
3x + 1
b)
x + 2
c)
3x + 7
d)
7x + 2
69.
Factor
x2 +17x - 60
x2 +17x - 60
a)
(x - 20)(x + 3)
b)
(x + 12)(x - 5)
c)
(x - 12)(x + 5)
d)
(x + 20)(x - 3)
70.
Factor:
x2 + 6x + 20
x2 + 6x + 20
a)
(x + 4)(x + 5)
b)
(x + 20)(x + 1)
c)
(x + 10)(x + 2)
d)
PRIME
71.
Factor:
x2 - 8x - 128
x2 - 8x - 128
a)
(x - 16)2
b)
(x - 16)(x + 8)
c)
(x + 16)(x - 8)
d)
(x - 16)(x - 8)
72.
Factor
4b5+4b3+16b2
4b5+4b3+16b2
a)
4b3(b4+b2+4b)
b)
4b3(b4+4b+5)
c)
4(b5+b3+4b2)
d)
4b2(b3+b+4)
73.
factor:x2 - 25
a)
( x + 5 ) ( x - 5 )
b)
( x - 5 ) ( x - 5 )
c)
( x + 5 ) ( x + 5 )
d)
Prime
74.
Factor:
56a3-8a
56a3-8a
a)
8a2(56a3-8a)
b)
8a(7a2-1)
c)
8a(7a3-a)
d)
8a2(35a2-a)
75.
Solve
4m2 - 100 = 0
4m2 - 100 = 0
a)
m=25 or m=-25
b)
m=96
c)
m=5 or m = -5
d)
m=-96
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