Free Printable Graphing Polynomials Review

1.

What is the DEGREE of this polynomial: $f\left(x\right)=-7x^3+2x^4-11x+3$

a)

0

b)

1

c)

3

d)

4

e)

8

2.

Identify the type of symmetry based on the graph:

i. symmetric with respect to the x-axis

ii. symmetric with respect to the y-axis

iii. symmetric with respect to the origin

a)

i only

b)

ii only

c)

iii only

d)

i, ii, and iii

3.

Identify the type of symmetry based on the graph:

i. symmetric with respect to the x-axis

ii. symmetric with respect to the y-axis

iii. symmetric with respect to the origin

a)

i only

b)

ii only

c)

iii only

d)

i, ii, and iii

4.

Which classification is given to a function that exhibits symmetry over the y-axis?

a)

odd

b)

even

5.

Which classification is given to a function that exhibits symmetry over the origin?

a)

odd

b)

even

6.

Use the symmetry tests to determine tif the given function is odd, even, or neither: $f\left(x\right)=x^5+1$

a)

odd

b)

even

c)

neither

7.

Is this an even, odd, or neither function?

f(x) = x⁴ + x²

a)

Even

b)

Odd

c)

Neither

8.

$y=7x^8-9x^2+33$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

9.

$y=8x^{12}-8x^4+6x+22$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

10.

$y=12x^7+6x^5-8x^3+4x$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

11.

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

12.

If the there is a turning point on the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

13.

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

14.

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

15.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

16.

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

a)

0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

b)

2 (Mult of 3), 7 (mult 1)

c)

0, 2, 7

d)

2 (mult of 2), 7 (mult of 3)

17.

a)

Even Degree
- Leading Coeff.

b)

Even Degree
+ Leading Coeff.

c)

Odd Degree
- Leading Coeff.

d)

Odd Degree
+ Leading Coeff.

18.

a)

Even Degree
- Leading Coeff.

b)

Even Degree
+ Leading Coeff.

c)

Odd Degree
- Leading Coeff.

d)

Odd Degree
+ Leading Coeff.

19.

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

a)

0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

b)

2 (Mult of 3), 7 (mult 1)

c)

0, 2, 7

d)

2 (mult of 2), 7 (mult of 3)

20.

Select polynomial whose zeros and degree are given.

Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4 with Degree: 7

a)

(x + 5)³(x - 9)²(x + 2)(x - 4)

b)

(x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

c)

(x + 5)³(x - 9)²(x + 2)

d)

(x + 5)(x - 9)(x + 2)(x - 4)

21.

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

a)

Degree: 6

b)

Degree: 5

c)

Degree: 3

d)

Degree: 2

22.

Please select the solution that describes if zeros crosses or turns at the x-axis for each x-intercept.

a)

2 crosses, 1 crosses, -3 turns, -4 turns

b)

1 crosses, -3 turns, - 4 crosses

c)

1 crosses, -3 turns, -4 turns

d)

1 turns, -3 crosses, -4 crosses

23.

What is the

y-intercept of the polynomial

y = 2(x + 1)(x + 2)(x - 3)?

a)

(0,-12)

b)

(0,12)

c)

(0,8)

d)

(0,2)

24.

What is the degree of the function graphed here?

a)

2

b)

3

c)

4

d)

5

25.

How many real zeros are shown in the graph?

a)

1

b)

2

c)

3

d)

4

26.

Find the choice that is correct

a)

The leading coefficient is 2, the degree is 4

b)

The leading coefficient is 3, the degree is 2

c)

The leading coefficient is 3, the degree is 4

d)

The leading coefficient is 2, the degree is 2.

27.

Which function has zeros: x=0, x=5(multiplicity of 3) and x=-6.

a)

f(x) = 9x(x + 5)³(x - 6)

b)

f(x) = 3(x - 5)³(x + 6)

c)

f(x) = -7x(x - 5)³(x + 6)

d)

f(x) = (x - 3)(x - 5)(x + 6)

28.

Which one of these are not a zero of $f\left(x\right)=x^2\left(x-1\right)^2\left(x+5\right)$ ?

a)

0

b)

1

c)

-5

d)

-1

29.

Which one of these are not a zero of $f\left(x\right)=-2x\left(3x+1\right)^2\left(x+7\right)^7$

a)

-2

b)

0

c)

$-\frac{1}{3}$

d)

-7

30.

What is the multiplicity of the zero x=1 for the function $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$ ?

a)

2

b)

1

c)

4

d)

3

31.

What is the multiplicity of the zero x=-5 for the function $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$ ?

a)

1

b)

2

c)

3

d)

4

32.

How does a multiplicity of 2 affect the graph?

a)

cross

b)

bounce

c)

wiggle (change direction)

33.

How does a multiplicity of 1 affect the graph?

a)

bounce

b)

cross

c)

wiggle (change direction)

34.

A polynomial function has zeros at -1,2, and 7 (all multiplicity of 1). Write a function rule that could represent this function.

a)

$f\left(x\right)=\left(x+1\right)\left(x-2\right)\left(x-7\right)$

b)

$f\left(x\right)=\left(x-1\right)\left(x+2\right)\left(x+7\right)$

c)

$f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^2\left(x-7\right)^2$

d)

$f\left(x\right)=\left(x-1\right)^2\left(x+2\right)^2\left(x+7\right)^2$

35.

A polynomial function has zeros at 5 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function rule that could represent this function.

a)

$f\left(x\right)=x^4\left(x-5\right)^2\left(x-3\right)$

b)

$f\left(x\right)=x^4\left(x+5\right)^2\left(x+3\right)$

c)

$f\left(x\right)=x\left(x-5\right)^4\left(x-3\right)^2$

d)

$f\left(x\right)=x\left(x+5\right)^2\left(x+3\right)^4$

36.

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

37.

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

38.

What is the degree of the polynomial?

a)

2

b)

3

c)

4

d)

5

39.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

40.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

41.

Which function has this end behavior?

a)

-x²-3x+1

b)

-x³+2x²+3

c)

x⁴+3x³-4x+1

d)

x⁵-4x⁴+2x²-1

42.

Which function has this end behavior?

a)

-1x⁴-3x³+3

b)

-2x⁷+2x⁴+4

c)

3x⁸+3x⁵-4x+7

d)

4x⁵-4x⁴+2x³-9

43.

Select all the even degree functions.

a)

A

b)

B

c)

C

d)

D

44.

Which functions have a negative leading coefficient?

a)

A

b)

B

c)

C

d)

D

45.

Which of the following is NOT a solution to f(x)=3x(x-8)(2x+1)²?

a)

0

b)

-1/2

c)

1/2

d)

8

46.

Which equation MOST LIKELY matches the graph?

a)

y = x⁴- x³ + 3x² + 2

b)

y = -x⁴ + x³ + 5x + 2

c)

y = x³ - 2x² + 1x + 3

d)

y = -x³ - 2x² + 1x + 3

47.

In the above graph, which root has a multiplicity of 2?

a)

-1

b)

-3

c)

-120

d)

4

48.

Find the local maximum and minimum

a)

Local max at x = -3

Local min at x = -3

b)

Local max at x = 1

Local min at x = -3

c)

Local max at x = -3

Local min at x = 1

d)

$\left(-\infty,\ \infty\right)$

49.

Identify the local minimum

a)

x = 8

b)

x = 4

c)

$\infty$

d)

x = 2

50.

Identify the global (or absolute) maximum.

a)

-2

b)

1

c)

$\infty$

d)

$-\infty$

51.

What is the location of the absolute maximum for the graphed function?

a)

x = 1

b)

x = 3

c)

x = 4

d)

x = 5

e)

Does Not Exist

52.

What is the value of the absolute minimum for the following function?

f\left(x\right)=\left(x-2\right)^2-4

a)

x = -4

b)

x = 0

c)

x = 2

d)

x = 4

e)

Does Not Exist

53.

What is the location of the relative maximum within the given interval of the graphed function?

-5\le x\le0

a)

x = -4

b)

x = -2

c)

x = 0

d)

x = 3

e)

Does Not Exist

54.

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)

55.

How many extrema are there in this graph?

a)

2 max, 2 min

b)

3 max, 2 min

c)

2 man, 3 min

d)

3 increasing intervals, 2 decreasing intervals

e)

2 increasing intervals, 3 decreasing intervals

56.

How many extrema (max and mins) are in the picture?

a)

2

b)

3

c)

4

d)

5

57.

What is the relative max?

a)

x = 0

b)

x = -2.55

c)

(-∞, ∞)

d)

None

Graphing Polynomials Review

Total questions: 57

Worksheet time: 2hrs 41mins

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