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Worksheets

Polynomial Graphs

Total questions: 48

Worksheet time: 3hrs 13mins

Name
Class
Date
1.
Describe the end behavior of
f(x) = -5x4 - 2x2 + 8
a)
Left side: Rises  
 Right side: Rises
b)
Left Side:  Rises
Right side: Falls
c)
Left side: Falls
Right side: Rises
d)
Left side: Falls
Right side: Falls
2.
Write a 4th degree polynomial function with:
*a positive leading coefficient
*zeros: 9, 3, -2, 0
a)
y = x(x - 9)(x - 3)(x + 2)
b)
y = x(x + 9)(x + 3)(x - 2)
c)
y = -x(x - 9)(x - 3)(x + 2)
d)
y = -x(x + 9)(x + 3)(x - 2)
3.
What is the y-intercept?
f(x) = -x4 + x3 + 5x2 + x + 6
a)
-1
b)
1
c)
5
d)
6
4.
What degree is the function?
a)
1
b)
2
c)
4
d)
10
5.
Is the leading coefficient positive or negative
a)
positive
b)
negative
6.

Even or Odd degree?

a)

even

b)

odd

7.
What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?
a)
-4, -1, 3
b)
3, -3, 4, 1
c)
4, 1, -3
d)
3, -4, -1, 3
8.
Describe the end behavior of
f(x) = -5x4 - 2x2 + 8
a)
Left side: Rises  
 Right side: Rises
b)
Left Side:  Rises
Right side: Falls
c)
Left side: Falls
Right side: Rises
d)
Left side: Falls
Right side: Falls
9.
Describe the end behavior of
f(x) = 2x2 + 6x5 + 10x
a)
Left side:  Rises
Right side: Rises
b)
Left side: Falls
Right side: Rises
c)
Left side:Rises
Right side: Falls
d)
Left side: Falls
Right side: Falls
10.

Identity the domain and the range of the linear graph.

a)

D= (∞, - ∞)

R= (∞, - ∞)

b)

D= (-∞, ∞)

R= (0, 2)

c)

D= (-∞, ∞)

R= (-∞, ∞)

d)

none of the above

11.

Identify the coordinates of the y-intercept.

a)

(0,1)

b)

(1,0)

c)

(0,0)

d)

There is not a y-intercept

12.

The end behavior of the following is graph is ______________ .

a)

x → −∞, y → ∞

x → ∞, y → ∞

b)

x → −∞, y → - ∞

x → ∞, y → ∞

c)

x → −∞, y → - ∞

x → ∞, y → - ∞

d)

none of the above

13.
What is the degree of the polynomial function
P(x)=3x4-7x2-2x7-x+4?
a)
4
b)
7
c)
2
d)
1
14.
In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____
a)
-∞
-∞
b)
+∞
-∞
c)
-∞
+∞
d)
+∞
+∞
15.
The polynomial is...
a)
Odd degree, positive leading coefficient.
b)
Odd degree, negative leading coefficient.
c)
Even degree, positive leading coefficient.
d)
Even degree, negative leading coefficient.
16.

For the given polynomial graph, which is the relative maximum?

a)

(1,8)

b)

(2,1)

c)

(1,2)

d)

(-1,-2)

17.

How would you describe the point at (0,6)?

a)

Relative Minimum

b)

Absolute Minimum

c)

Relative Maximum

d)

Absolute Maximum

18.

How would you describe the point at (0,6)?

a)

Relative Minimum

b)

Absolute Minimum

c)

Relative Maximum

d)

Absolute Maximum

19.

Which of the following does this graph not have?

a)

absolute max

b)

absolute min

c)

relative max

d)

relative min

20.

Which of the following does this graph not have?

a)

absolute max

b)

absolute min

c)

relative max

d)

relative min

21.

What is the Range of the function being graphed?

a)

(-∞, ∞)

b)

[7, ∞)

c)

(-∞, 7]

d)

(-1, 1)

e)

(-∞, 7)

22.

What is the Domain of the function being graphed?

a)

(-∞, ∞)

b)

[7, ∞)

c)

(-∞, 7]

d)

(-1, 1)

e)

(-∞, 7)

23.

What is the absolute minimum point on the polynomial graph?

a)

There is not an absolute minimum

b)

(-4,-1.5)

c)

(-1.5,-4)

d)
24.
What is the range of the function?
a)
[-1, +∞)
b)
(-1,1)
c)
[1.5, +∞)
d)
(-2, 2)
25.
What is the range of the function?
a)
[-1, +∞)
b)
(-1,1)
c)
[1.5, +∞)
d)
(-2, 2)
26.
What is the maximum number of roots for
 
 8x7 - 6x5 + 4x3 + 2x + 1 = 0
a)
4
b)
6
c)
7
d)
16
27.
What is the domain of the function?
a)
All Real Numbers
b)
-3 ≤ x ≤ 1
c)
y ≥ 4
d)
y ≤ 4
28.
What is the range of this function?
a)
-4 ≤ y ≤ 5
b)
-1 ≤ x ≤ 3
c)
All Real Numbers
d)
y ≥ -4
29.
What is the degree?
a)
Positive
b)
Negative
c)
Odd
d)
Even
30.

What is the interval of decrease for Graph #8?

a)

(-∞, 0) ∪ (2, ∞)

b)

(0, 2)

c)

(-∞, 2)

d)

(2, ∞)

31.

What is the interval of decrease for Graph #8?

a)

(-∞, 0) ∪ (2, ∞)

b)

(0, 2)

c)

(-∞, 2)

d)

(2, ∞)

32.

How many increasing and decreasing intervals are there in this graph?

a)

2 increasing, 2 decreasing

b)

1 increasing, 2 decreasing

c)

2 increasing, 1 decreasing

d)

1 increasing, 1 decreasing

33.

What are the increasing and decreasing intervals of the graph?

a)

Increasing = (-1.5, 0) & (1.5, ∞)

Decreasing = (-∞, -1.5) & (0, 1.5)

b)

Increasing = (-∞, -1.5) & (0, 1.5)

Decreasing = (-1.5, 0) & (1.5, ∞)

c)

Increasing = (-∞, -1.5) & (1.5, ∞)

Decreasing = (-1.5, 0) & (0, 1.5)

d)

Increasing = (-1.5, 0) & (0, 1.5)

Decreasing = (-∞, -1.5) & (1.5, ∞)

34.

What are the increasing intervals?

a)

(- ∞, 0) & (2, ∞ )

b)

(-1, 0) & (2,4)

c)

(0,2) & (-3, -7)

d)

(-8, -3) & (-7, 8)

35.

What are the decreasing intervals on the graph?

a)

(-∞, 0) & (-4, ∞)

b)

(-∞, -1) & (1, ∞)

c)

(-∞, -2) & (2, ∞)

d)

(-∞, 0) & (4, ∞)

36.

What are the increasing and decreasing intervals of the graph?

a)

Increasing = (-∞,-3), (-1,2), (4, ∞)

Decreasing = (-3,-1), (2,4)

b)

Increasing = (-3,-1), (2,4)

Decreasing = (-∞,-3), (-1,2), (4, ∞)

c)

Increasing = (-∞,-3), (-1,2),

Decreasing (-3,-1), (2,4), (4, ∞)

d)

Increasing = (-∞, 2), (-3, 1), (-1, ∞)

Decreasing (2, -3), (1, -1)

37.

Identify where the function is decreasing.

a)

x < -4 , x > 1

b)

-4 < x < 1

c)

-6 < x < 7.5

d)

All Real Numbers

38.
When is this function increasing?
a)
−2.5 < x < 2.5
b)
0 < x < 5
c)
0 < x < 55
d)
−5 < x < 0
39.

Identify the decreasing interval:

a)

(0, 4)

b)

(1, 0) U (1, 4)

c)

(-1, 1)

d)

(-∞, -1) U (1, ∞)

40.

What are the extrema of the graph?

a)

Max = (2, -3), (1, 2)

Min = (-3, -1), (-1, 4)

b)

Max = (-3, -1), (-1, 4)

Min = (2, -3), (1, 2)

c)

Max = (-1, -3), (4, -1)

Min = (-3, 2), (2, 1)

d)

Max = (-3, 2), (2, 1)

Min = (-1, -3), (4, -1)

41.
When is this function increasing?
a)
−2.5 < x < 2.5
b)
0 < x < 5
c)
0 < x < 55
d)
−5 < x < 0
42.
Find the zeros of the polynomial.
f(x) = (x-5)(2x+3)(7x-4)(x+6)
a)
x = 5, (2/3), 6, (7/4)
b)
x= -5, (3/2), (-4/7), 6
c)
x= 5, (-3/2), (4/7), -6
d)
x= 6, 5, -2/3, -4/7
43.

If the zeros of a polynomial are -1, 3, and 7 then what does the polynomial look like in factored form?

a)

(x-1)(x+3)(x+7)

b)

(x+1)(x-3)(x-7)

c)

-x2 + 3x + 7

d)

(x-1)

44.

If the zeros of a polynomial are -1, 3, and 7 then what does the polynomial look like in factored form?

a)

(x-1)(x+3)(x+7)

b)

(x+1)(x-3)(x-7)

c)

-x2 + 3x + 7

d)

(x-1)

45.

What are the zeros in (x-5)(x+4)

a)

4 and -5

b)

5 and -4

c)

-4 and -5

d)

no zeros

46.
Determine the roots of the polynomial. 
f(x) = -x(x+1)(x-3)
a)
-1, 3
b)
0, -1, 3
c)
1, -3
d)
0, -3, 1
47.
What is the y-intercept?
f(x) = -x4 + x3 + 5x2 + x + 6
a)
-1
b)
1
c)
5
d)
6
48.

State the y-intercept.

y = 2x5 + 3x4 – 5x2 + 3x

a)

-90

b)

90

c)

3

d)

0