Search Header Logo
End Behavior/Multiplicity  of a Polynomial Function

End Behavior/Multiplicity of a Polynomial Function

Assessment

Presentation

Mathematics

9th - 12th Grade

Medium

Created by

Nicole Stanziale

Used 4+ times

FREE Resource

25 Slides • 36 Questions

1

End Behavior of a Polynomial Function

media

2

Standard Form of a Polynomial

  • List the terms by degrees in DESCENDING order

  • The following 2 minute video shows an example

3

4

Multiple Choice

Which of the following polynomials is written in STANDARD form?

1

3x212x+4x33x^2-12x+4x^3

2

4x3+3x212x4x^3+3x^2-12x

5

Multiple Choice

Which of the following polynomials is written in STANDARD form?

1

4x5+2-4x^5+2

2

24x52-4x^5

6

Leading Coefficient

7

Multiple Choice

What is the leading coefficient   6x32x2+12x76x^3-2x^2+12x-7  

1

6

2

3

3

-2

4

12

5

1

8

Fill in the Blank

Name the leading coefficient 7x2+3x5-7x^2+3x-5  

9

media

10

Even Degree Polynomials

  • Polynomials with an EVEN degree will always end in the same direction.

  • UP if the Leading Coefficient is POSITIVE

  • DOWN if the Leading Coefficient is NEGATIVE

media

11

media

12

media

13

media

14

Multiple Select

Select ALL Even Degree Functions.

1
2
3
4

15

Odd Degree Polynomials

  • Polynomials with an ODD degree will always in in opposite directions (one up, one down).

  • If the Leading Coefficient is POSITIVE, the polynomial will go up to the right and down to the left.

  • If the Leading Coefficient is NEGATIVE, the polynomial will go down to the right and up to the left.

media

16

media

17

media

18

Multiple Choice

Which polynomial has an ODD degree?

1

3x25x+13x^2-5x+1

2

2x3+4x2+6x82x^3+4x^2+6x-8

19

Multiple Select

Select all the polynomials that have an odd degree.

1

6x3+8x16x^3+8x-1  

2

4x65x3+2x2+8x14x^6-5x^3+2x^2+8x-1  

3

x2+7x3x^2+7x-3  

4

x+5x+5  

5

x52x2x^5-2x^2  

20

End Behavior

The guy on this 3 minute long video is super goofy, but his information is good!

media

21

22

23

media

24

Multiple Choice

What is the degree of this polynomial? 3x4 + 2x35x2+10x7-3x^4\ +\ 2x^3-5x^2+10x-7

1

1

2

2

3

3

4

4

5

5

25

Multiple Choice

Is the degree of this polynomial ODD or EVEN? 3x4 + 2x35x2+10x7-3x^4\ +\ 2x^3-5x^2+10x-7

1

ODD

2

EVEN

26

Multiple Choice

Is the leading coefficient of this polynomial POSITIVE or NEGATIVE? 3x4 + 2x35x2+10x7-3x^4\ +\ 2x^3-5x^2+10x-7

1

POSITIVE

2

NEGATIVE

27

Poll

Describe the END BEHAVIOR of this polynomial 3x4 + 2x35x2+10x7-3x^4\ +\ 2x^3-5x^2+10x-7

Both sides go up

Both sides go down

Left up and right down

Left down and right up

28

Multiple Choice

Describe the END BEHAVIOR of this polynomial x67x5+x32x^6−7x^5+x^3−2

1

Both sides go up

2

Both sides go down

3

Left up and right down

4

Left down and right up

29

Multiple Choice

Question image

What do you know about the rule (equation) of the polynomial based on its graph?

1

Leading coefficient is positive, degree is even

2

Leading coefficient is negative, degree is even

3

Leading coefficient is positive, degree is odd

4

Leading coefficient is negative, degree is odd

30

Examples

The following slides show examples of polynomials of various degrees and leading coefficients.

31

media

32

media

33

media

34

35

Multiple Choice

A polynomial with an EVEN degree will have...

1

the ends going the same direction

2

the ends going in different direction

36

Multiple Choice

A polynomial with an ODD degree will have...

1

the ends going the same direction

2

the ends going in different direction

37

Multiple Choice

A Quadratic equation with a negative Leading Coefficient will have

1

both end going up

2

both ends going down

3

the left down and the right up

4

the left up and the right down

38

Multiple Choice

Question image

Does this graph represent a polynomial with an ODD or EVEN degree?

1

Odd

2

Even

39

Multiple Choice

Question image

Is the Leading Coefficient of this CUBIC polynomial POSITIVE or NEGATIVE?

1

Positive

2

Negative

40

Multiple Choice

Question image

Does this graph represent a polynomial with an ODD or EVEN degree?

1

Odd

2

Even

41

Multiple Choice

Question image

Is the Leading Cofficient of the QUARTIC polynomial POSITIVE or NEGATIVE?

1

Positive

2

Negative

42

Multiple Choice

Which of the following graphs represents a polynomial that has a POSITIVE leading coefficient and EVEN degree?

1
2
3
4

43

Multiple Choice

Which of the following graphs represents a polynomial that has a NEGATIVE leading coefficient and EVEN degree?

1
2
3
4

44

Multiple Choice

Which of the following graphs represents a polynomial that has a POSITIVE leading coefficient and ODD degree?

1
2
3
4

45

Multiple Choice

Which of the following graphs represents a polynomial that has a NEGATIVE leading coefficient and ODD degree?

1
2
3
4

46

End Behavior Notation

media

47

Multiple Choice

Question image

Please complete the end behavior function notation as x+, f(x) as\ x\rightarrow+\infty,\ f\left(x\right)\ \rightarrow

1

++\infty  

2

-\infty  

48

Multiple Choice

Question image

Please complete the end behavior function notation as x, f(x) as\ x\rightarrow-\infty,\ f\left(x\right)\ \rightarrow

1

++\infty  

2

-\infty  

49

Multiple Choice

Question image

Please complete the end behavior function notation as x+, f(x)as\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow

1

++\infty  

2

-\infty  

50

Multiple Choice

Question image

Please complete the end behavior function notation as x, f(x)as\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow

1

++\infty  

2

-\infty  

51

Multiple Choice

Question image

Please complete the end behavior function notation as x, f(x)as\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow

1

++\infty  

2

-\infty  

52

Multiple Choice

Question image

Please complete the end behavior function notation as x+, f(x)as\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow

1

++\infty  

2

-\infty  

53

REAL Zeroes

  • Indicates how many times the function crosses the x axis.

  • There are 6 real zeros in this example.

media

54

REAL Zeroes, continued

  • This polynomial with a positive Leading Coefficient and odd degree (d=5) has 3 real zeroes.

  • There are 2 imaginary zeroes

  • The total number of zeroes (real + imaginary) will equal the degree

media

55

Multiple Choice

Question image

How many REAL zeroes are shown in this polynomial function?

1

0

2

1

3

2

4

3

5

4

56

Multiple Choice

Question image

How many REAL zeroes are shown in this polynomial function?

1

0

2

1

3

2

4

3

5

4

57

Open Ended

Question image

How many REAL zeroes are shown in this polynomial function?

58

Turning Points

  • A turning point is where a graph "turns around" , that is changes from increasing to decreasing or from decreasing to increasing.

  • A polynomial function of degree n has at most n-1 turning points, and at most n x-intercepts.

  • If the function has n distinct real roots, then it has exactly n-1 turning points and exactly n x-intercepts.

59

Multiple Choice

How many turning points will a quartic function with four real zeros have?

1

1

2

2

3

3

4

4

60

Multiple Choice

Question image

Which function could describe this graph?

1
2
3
4

61

Open Ended

What questions do you have for me?

End Behavior of a Polynomial Function

media

Show answer

Auto Play

Slide 1 / 61

SLIDE