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Characteristics of Polynomial Graphs

Total questions: 40

Worksheet time: 10hrs 0mins

Name
Class
Date
1.
a)
(-2.55, 0), (2.55, 0)
b)
(-3, 0), (-2, 0), (2, 0), (3, 0)
c)
(0, 36)
d)
(0, -3), (0, -2), (0, 2), (0, 3)
2.
a)
A.
b)
B.
c)
C.
d)
D.
3.

At what x-value does a relative maximum occur?

a)

1

b)

4

c)

-1

d)

2

4.

At what x-value does a relative minimum occur?

a)

1

b)

2

c)

0

d)

-1

5.

Describe the end behavior of

f(x) = -5x4- 2x2 + 8

a)

Left side: UP

Right side: UP

b)

Left Side: Up

Right side: Down

c)

Left side: Down

Right side: Up

d)

Left side: Down

Right side: Down

6.

Describe the end behavior of

f(x) = 2x2 + 6x5 + 10x

a)

Left side: Up

Right side: Down

b)

Left side: Down

Right side: Up

c)

Left side: Up

Right side: Down

d)

Left side: Down

Right side: Down

7.
a)
4th degree polynomial with a positive leading coefficient
b)
4th degree polynomial with a negative leading coefficient
c)
3rd degree polynomial with a positive leading coefficient
d)
3rd degree polynomial with a negative leading coefficient
8.

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

9.
In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____
a)
-∞
-∞
b)
+∞
-∞
c)
-∞
+∞
d)
+∞
+∞
10.
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.
11.
Find the zeros.
a)
x = 0 and 4
b)
x = 0 and -4
c)
x = 0
d)
x = -4
12.
What is the degree of the polynomial:
f(x) = 3x2 + 4x - 5
a)
Degree 2  (quadratic)
b)
Degree 3 (cubic)
c)
Degree 4 (quartic)
d)
Degree 5 (quintic)
13.

What type of polynomial could be represented by this graph?

a)

Even Degree

- Leading Coefficient

b)

Even Degree

+ Leading Coefficient

c)

Odd Degree

- Leading Coefficient

d)

Odd Degree

+ Leading Coefficient

14.
What is the degree of the polynomial 3x4 + 2x2 + 5x ?
a)
1
b)
2
c)
3
d)
4
15.
What is the degree of the polynomial 17x + 4
a)
0
b)
1
c)
2
d)
3
16.
What type of polynomial is this and what is its degree?
5b3 - 3 + 6b 
a)
3rd degree binomial
b)
3rd degree monomial
c)
3rd degree trinomial
d)
1st degree polynomial
17.
What is the constant in the polynomial?
-2xyz + 3x2 - 2y2 - 6z2 + 32
a)
-2
b)
3
c)
-6
d)
32
18.
When a polynomial is written in standard form, the coefficient of the first term is called the _____________.
a)
Boss coefficient
b)
Leading coefficient
c)
Best coefficient
d)
Greatest common coefficient
19.
The following polynomial is written in standard form:
7x3 - 11x2 + 8x - 5
a)
True
b)
False
20.
What is the leading coefficient of the polynomial?
  9x5 + 2x4 - x3 + 9x2 - 2
a)
5
b)
9
c)
2
d)
4
21.
What kind of leading coefficient does the function have?
  f(x) = -2x2 + 4x - 7
a)
positive
b)
negative
22.
What kind of leading coefficient does the function have?
  f(x) = 4x4 + 6x3 - x
a)
positive
b)
negative
23.

Use the end behavior to determine whether the leading coefficient is positive or negative and whether the degree is even or odd.

a)

Leading Coefficient Positive

Degree - Even

b)

Leading Coefficient Positive

Degree - Odd

c)

Leading Coefficient Negative

Degree - Even

d)

Leading Coefficient Negative

Degree - Odd

24.

Use the end behavior to determine if the leading coefficient is positive or negative and whether the degree is even or odd.

a)

Leading Coefficient Positive

Degree - Even

b)

Leading Coefficient Positive

Degree - Odd

c)

Leading Coefficient Negative

Degree - Even

d)

Leading Coefficient Negative

Degree - Odd

25.

Use the degree and the leading coefficient to determine the end behavior.

f(x) = 2x3 - x + 5

a)

Left up, Right up

b)

Left up, Right down

c)

Left down, Right up

d)

Left down, Right down

26.

Determine the end behavior of the polynomial by identifying the degree and leading coefficient.


f(x) = 5x4 - x + 6

a)

UP-UP

b)

UP-DOWN

c)

DOWN-UP

d)

DOWN-DOWN

27.

Use the degree and the leading coefficient to determine the end behavior.

f(x) = -x5 - 4x +2

a)

Left up, Right up

b)

Left up, Right down

c)

Left down, Right up

d)

Left down, Right down

28.

Use the end behavior to determine if the leading coefficient is positive or negative and whether the degree is even or odd.

a)

Leading Coefficient Positive

Degree - Even

b)

Leading Coefficient Positive

Degree - Odd

c)

Leading Coefficient Negative

Degree - Even

d)

Leading Coefficient Negative

Degree - Odd

29.

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→ -∞

30.

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→ -∞

31.

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→ -∞

32.
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
33.
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
34.
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) →-∞.
35.

How many turning points does the function have?

a)

2

b)

3

c)

4

d)

5

36.

At what x-value does the relative maxima occur?

a)

2.5

b)

8

c)

3

d)

5

37.
Which of the following statement are false.
a)
There is a relative min at the point (8,0)
b)
There is another relative min at the point (0,-7.5)
c)
There is a relative max at the point (5,2.5)
d)
There are more relative maximums than there are relative minimums.
38.
Fill in the blank:  The maximum number of turning points is ____ less than the degree of the polynomial.
a)
0
b)
1
c)
2
d)
3
39.
What is the maximum number of turning for the function f(x) = 8x3-27
a)
0
b)
1
c)
2
d)
3
40.
What is the maximum number of turning points for the function?
f(x) = -x5 - 4x +2
a)
1
b)
2
c)
3
d)
4

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