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McCaa End Behavior and Transformation

Total questions: 77

Worksheet time: 4hrs 24mins

Name
Class
Date
1.
The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
2.
The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
3.
The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
4.
In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____
a)
-∞
-∞
b)
+∞
-∞
c)
-∞
+∞
d)
+∞
+∞
5.
In the above graph complete the following end behavior: (f(x)=y)
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____
a)
-∞
-∞
b)
+∞
-∞
c)
-∞
+∞
d)
+∞
+∞
6.

Describe the end behavior of the graph.

a)

x → -∞, f(x) → ∞ and x→∞, f(x) →⁻∞

b)

x → -∞, f(x) → ∞ and x→∞, f(x) →∞

c)

x → -∞, f(x) → ∞ and x→∞, f(x) → 0

d)

x → -∞,f(x) → -∞and x→ ∞, f(x) → ∞

7.
What is the degree of the polynomial?
a)
2
b)
3
c)
4
d)
5
8.
Describe the end behavior of the graph.
a)
x → ∞, y→ ∞ and
x→ ∞, y→⁻∞
b)
x → ∞, y→ ∞ and
x→⁻∞, y→∞
c)
None of these
d)
x →∞,y→⁻∞ and
x→∞, y→⁻∞
9.
Describe the end behavior of the graph.
a)
x → ∞, y→ ∞ and x→∞, y→⁻∞
b)
x → ∞, y→ ∞ and x→⁻∞, y→∞
c)
x → ∞, y→ ∞ and x→⁻∞, y→ 0
d)
x → ∞,y→ ∞and x→ ⁻∞, y→ ⁻∞
10.
Describe the end behavior of the graph.
a)
x →∞, y→⁻∞ and x →⁻∞,y→⁻∞
b)
x →∞, y→∞ and x→⁻∞, y→∞
c)
x →∞, y→∞ and x→⁻∞, y→0
d)
x →∞,y→∞ and x→⁻∞, y→⁻∞
11.
Describe the end behavior of the graph.
a)
x →∞, y→∞ and x→∞, y→⁻∞
b)
x →∞, y→∞ and x→⁻∞, y→∞
c)
x →∞, y→∞ and x→⁻∞, y→0
d)
x →∞,y→0 and x→∞, y→⁻∞
12.
Describe the end behavior of the graph.
a)
x → ∞, y→ ∞ and
x→ ∞, y→⁻∞
b)
x → ∞, y→ ∞ and
x→⁻∞, y→∞
c)
None of these
d)
x →∞,y→⁻∞ and
x→∞, y→⁻∞
13.
Describe the end behavior of the graph.
a)
x → ∞, y→ ∞ and x→∞, y→⁻∞
b)
x → ∞, y→ ∞ and x→⁻∞, y→∞
c)
x → ∞, y→ ∞ and x→⁻∞, y→ 0
d)
x → ∞,y→ ∞and x→ ⁻∞, y→ ⁻∞
14.
Describe the end behavior of the graph.
a)
x →∞, y→⁻∞ and x →⁻∞,y→⁻∞
b)
x →∞, y→∞ and x→⁻∞, y→∞
c)
x →∞, y→∞ and x→⁻∞, y→0
d)
x →∞,y→∞ and x→⁻∞, y→⁻∞
15.
Describe the end behavior of the graph.
a)
x →∞, y→⁻∞ and x →⁻∞,y→⁻∞
b)
x →∞, y→∞ and x→⁻∞, y→∞
c)
x →∞, y→∞ and x→⁻∞, y→2
d)
x →∞,y→2 and x→⁻∞, y→∞
16.
The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
17.
The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
18.
The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
19.
The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
20.
In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____
a)
-∞
-∞
b)
+∞
-∞
c)
-∞
+∞
d)
+∞
+∞
21.
In the above graph complete the following end behavior: (f(x)=y)
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____
a)
-∞
-∞
b)
+∞
-∞
c)
-∞
+∞
d)
+∞
+∞
22.
Using the above graph what is the sign of the leading coefficient?
a)
Positive
b)
Negative
23.
Which function has this end behavior?
Note: f(x)=y
a)
-x2-3x+1
b)
-x3+2x2+3
c)
x4+3x3-4x+1
d)
x5-4x4+2x2-1
24.
Which function has this end behavior?
Note: f(x)=y
a)
-1x4-3x3+3
b)
-2x7+2x4+4
c)
3x8+3x5-4x+7
d)
4x5-4x4+2x3-9
25.
Determine the end behavior of the graph of 
f(x) = 3x4 + 2x - 5
Note: f(x)=y
a)
As x →∞, f(x) →∞.
As x→-∞, f(x) →-∞.
b)
As x →∞, f(x) →∞.
As x→-∞, f(x) →∞.
c)
As x →∞, f(x) →-∞.
As x→-∞, f(x) →∞.
d)
As x →∞, f(x) →-∞.
As x→-∞, f(x) →-∞.
26.
What is the degree of this polynomial function?  Is the leading coefficient positive or negative?
(Note: quartic means 4th degree, cubic means 3rd degree polynomials)
a)
A quartic polynomial with a negative leading coefficient.
b)
A quartic polynomial with a positive leading coefficient.
c)
A cubic polynomial with a negative leading coefficient.
d)
A cubic polynomial with a positive leading coefficient.
27.
Which one means left
a)
x →-∞
b)
x →∞
28.
Which one means up
a)
y →-∞
b)
y →∞
29.
Which one means the function goes up on the left
a)
x →-∞, y→∞
b)
x →-∞, y→-∞
30.
Which one means the function goes down on the left
a)
x →-∞, y→∞
b)
x →-∞, y→-∞
31.

what the is the end behavior

a)

Up, up

b)

up, down

c)

down, down

d)

down, up

32.

what the is the end behavior

a)

Up, up

b)

up, down

c)

down, down

d)

down, up

33.

what the is the end behavior

a)

Up, up

b)

up, down

c)

down, down

d)

down, up

34.

what the is the end behavior

a)

Up, up

b)

up, down

c)

down, down

d)

down, up

35.

what the leading coefficient

a)

Postive

b)

Negative

c)

Even

d)

Odd

36.

what the is the degree of the polynomial

a)

Postive

b)

Negative

c)

Even

d)

Odd

37.

what the is the Leading Coeffiecent and Degree

a)

Positive, Odd

b)

Negative, Odd

c)

Postive, Even

d)

Negative, Even

38.

what the is the leading coefficient and degree

a)

Postive, Odd

b)

Negative, Odd

c)

Postive, Even

d)

Negative, Even

39.
If the blue function is f(x)=x2, then the red function must be
a)
g(x)=x2-5
b)
g(x)=x2+5
c)
g(x)=(x-5)2
d)
g(x)=(x+5)2
40.
g(x)=f(x-1)-5
Describe the transformation to f(x) that results in g(x).
a)
f(x) has been translated to the left one and down five.
b)
f(x) has been translated to the right one and down five.
c)
f(x) has been translated to the left one and up five.
d)
f(x) has been translated to the right one and up five.
41.
Which transformation transforms the graph of
f(x) = x2 to the graph of g(x) = (x + 4)2?
a)
a vertical translation 4 units up
b)
a vertical translation 4 units down
c)
a horizontal translation 4 units to the left
d)
a horizontal translation 4 units to the right
42.

Given the parent function p(x)=cos(x), which phrase best describes the transformation used to obtain the graph of g(x)=cos(x+a) - b, if a and b are positive constants?

a)

Right a units, up b units

b)

Right a units, down b units

c)

Left a units, up b units

d)

Left a units, down b units

43.

Describe the transformation that occurred

p(x) = f(x + 3)

a)

Right 3 units

b)

Vertical Stretch

c)

Up 3 units

d)

Left 3 units

44.

Describe the transformation that occurred.

h(x) = f(x) + 2

a)

up 2 units

b)

left 2 units

c)

Vertical Strech

d)

right 2 units

45.

Describe the transformation that occurred.

w(x) = f(x - 7)

a)

Down 7

b)

Up 7

c)

Right 7

d)

vertical compression

46.

Describe the transformation that occurred

m(x) = f(x + 1)

a)

Left 1 Unit

b)

Right 1 unit

c)

vertical stretch

d)

up 1 unit

47.

Describe the transformation that occurred

k(x) = f(x) - 9

a)

vertical compression

b)

Down 9 units

c)

Left 9 units

d)

Right 9 Units

48.

Describe the transformation that occurred

g(x) =2f(x)

a)

Up 2 units

b)

vertical compression

c)

vertical stretch

d)

Right 2 Units

49.

Describe the transformation that occurred

h(x) = 1/5f(x)

a)

Up 5 Units

b)

vertical compression

c)

vertical stretch

d)

Down 5 Units

50.

Describe the transformation that occurred

t(x) = f(x) - 1

a)

Right 1 Unit

b)

Down 1 Unit

c)

vertical compression

d)

vertical stretch

51.

Describe the transformation that occurred

s(x) = 7f(x)

a)

vertical compression

b)

Up 7 Units

c)

Over 7 Units

d)

vertical stretch

52.
Describe the transformation that occurred 
d(x) = f(x) - 1
a)
Left 1 Unit
b)
Right 1 Unit
c)
Up 1 Unit
d)
Down 1 Unit
53.

vertical stretch, translation left 3

a)

½f(x + 3)

b)

4f(x - 3)

c)

4f(x) + 3

d)

4f(x + 3)

54.

translation up 1

a)

f(x) + 1

b)

f(x - 1)

c)

f(x) - 1

d)

f(x + 1)

55.

reflection over y-axis, shift right 1

a)

f(-x - 1)

b)

-f(x + 1)

c)

-f(x) - 1

d)

-f(x - 1)

56.

horizontal compression

a)

g(x) = 3f(x)

b)

g(x) = ½f(x)

c)

g(x) = f(¼x)

d)

g(x) = f(5x)

57.

vertical reflection, horizontal stretch

a)

g(x) = ½f(-x)

b)

g(x) = -f(¼x)

c)

g(x) = -3f(x)

d)

g(x) = -f(4x)

58.
Identify the transformations:
a)
Shrink of 2; up 5
b)
Stretch of 2; up 5
c)
Up 2; left 5
d)
Up 2; right 5
59.
a)
Left 2, Down 2, Vertical Stretch
b)
Right 2; Up 1; 
c)
Vertical Stretch; Right 2; Up 1
d)
Left 2; Down 2;
60.

The graph of f(x)=xf\left(x\right)=\sqrt{x} is transformed to create  g(x)=f(x+5)−1g\left(x\right)=f\left(x+5\right)-1 . Describe the graph of g(x) in relation to f(x). 

a)

shifted left 5 units

b)

shifted right 5 units

c)

shifted up 1 unit

d)

shifted down 1 unit

e)

reflection across the x-axis

61.

Describe the transformations for the following function h(x)=2(x−3)2+5h\left(x\right)=2\left(x-3\right)^2+5 from the parent function  g(x)=x2g\left(x\right)=x^2   


a)

vertical stretch times 2

b)

horizontal stretch times 2

c)

shift left 3 units

d)

shift up 5 units

e)

shift right 3 units

62.

Describe the transformation of f(x) to g(x) from the graph.

a)

shift left 2 units

b)

shift right 2 units

c)

vertical stretch

d)

horizontal stretch

63.

The graph of f(x)f\left(x\right) is transformed to create  g(x)=3f(x)g\left(x\right)=3f\left(x\right) . Which of the following describes the transformation?

a)

f(x) is translated 3 units left

b)

f(x) is vertically stretched by a factor of 3

c)

f(x) translated 3 units up

d)

f(x)  is horizontally stretched by a factor of 3

64.

f(x)=∣x∣+1f\left(x\right)=\left|x\right|+1  

a)

Left 1

b)

Right 1

c)

Up 1

d)

Down 1

65.

f(x)=∣x+1∣f\left(x\right)=\left|x+1\right|  

a)

Left 1

b)

Right 1

c)

Up 1

d)

Down 1

66.

f(x)=∣x−1∣f\left(x\right)=\left|x-1\right|  

a)

Left 1

b)

Right 1

c)

Up 1

d)

Down 1

67.

Which of the following square root curves have translated left 7?

a)

y=x−7y=\sqrt{x}-7

b)

y=x+7y=\sqrt{x}+7

c)

y=x−7y=\sqrt{x-7}

d)

y=x+7y=\sqrt{x+7}

68.

Which of the following square root curves have translated down 7?

a)

y=x−7y=\sqrt{x}-7

b)

y=x+7y=\sqrt{x}+7

c)

y=x−7y=\sqrt{x-7}

d)

y=x+7y=\sqrt{x+7}

69.

Which of the following square root curves have translated right 7?

a)

y=x−7y=\sqrt{x}-7

b)

y=x+7y=\sqrt{x}+7

c)

y=x−7y=\sqrt{x-7}

d)

y=x+7y=\sqrt{x+7}

70.

If a function has a horizontal transformation, how does it move?

a)

Up or Down

b)

Left or Right

c)

Reflects across the y-axis

d)

Does not move at all

71.

What is the function family for the following graph?

a)

Exponential

b)

Square Root

c)

Quadratic

d)

Absolute Value

72.
Describe the transformation
a)
left 2 up 5
b)
right 2 up 5
c)
left 2 down 5
d)
right 2 down 5
73.
Tell how the graph transformed.
y = (x - 3)2
a)
Translated right 3
b)
Translated left 3
c)
Translated up 3
d)
Translated down 9
74.
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
75.
Describe the transformation
a)
left 2 up 5
b)
right 2 up 5
c)
left 2 down 5
d)
right 2 down 5
76.
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
77.

How is the blue graph different from the red parent graph? Mark all that are true.

a)

shifted 1 unit up from the red parent graph

b)

shifted 2 units right from the red parent graph

c)

flipped over the x-axis from the red parent graph

d)

flipped over the y-axis from the red parent graph

e)

shifted 1 unit down from the red parent graph

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