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Identify the leading coefficient, degree, and end behavior. 1 ..., Study notes of Pre-Calculus

Western Suffolk BOCESPre-Calculus

Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient. Justify your answer.

Typology: Study notes

2021/2022

Uploaded on 09/12/2022

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Math 3 Unit 3 Worksheet 1
Math 3 Unit 3 Worksheet 1 Name:
End Behavior of Polynomial Functions Date: Per: ______
Identify the leading coefficient, degree, and end behavior.
1. ๐‘“๐‘“(๐‘ฅ๐‘ฅ)= 5๐‘ฅ๐‘ฅ2+ 7๐‘ฅ๐‘ฅ โˆ’ 3 2. ๐‘ฆ๐‘ฆ=โˆ’2๐‘ฅ๐‘ฅ2โˆ’3๐‘ฅ๐‘ฅ+ 4 3. ๐‘”๐‘”(๐‘ฅ๐‘ฅ)=๐‘ฅ๐‘ฅ3โˆ’9๐‘ฅ๐‘ฅ2+ 2๐‘ฅ๐‘ฅ+ 6
Degree: Degree: Degree:
Leading Coeff: Leading Coeff: Leading Coeff:
End Behavior: End Behavior: End Behavior:
4. ๐‘ฆ๐‘ฆ=โˆ’7๐‘ฅ๐‘ฅ3+ 3๐‘ฅ๐‘ฅ2+12๐‘ฅ๐‘ฅ โˆ’ 1 5. โ„Ž(๐‘ฅ๐‘ฅ)=โˆ’2๐‘ฅ๐‘ฅ7+ 5๐‘ฅ๐‘ฅ4โˆ’3๐‘ฅ๐‘ฅ 6. ๐‘”๐‘”(๐‘ฅ๐‘ฅ)= 8๐‘ฅ๐‘ฅ3+ 4๐‘ฅ๐‘ฅ2+ 7๐‘ฅ๐‘ฅ4โˆ’9๐‘ฅ๐‘ฅ
Degree: Degree: Degree:
Leading Coeff: Leading Coeff: Leading Coeff:
End Behavior: End Behavior: End Behavior:
Identify the end behavior. Justify your answer.
7. ๐‘“๐‘“(๐‘ฅ๐‘ฅ)= 4๐‘ฅ๐‘ฅ5โˆ’3๐‘ฅ๐‘ฅ4+ 2๐‘ฅ๐‘ฅ3 8. ๐‘ฆ๐‘ฆ=โˆ’๐‘ฅ๐‘ฅ4+๐‘ฅ๐‘ฅ3โˆ’ ๐‘ฅ๐‘ฅ2+ 1 โˆ’1 9. โ„Ž(๐‘ฅ๐‘ฅ)= 3๐‘ฅ๐‘ฅ6โˆ’7๐‘ฅ๐‘ฅ4โˆ’2๐‘ฅ๐‘ฅ9
Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
Justify your answer.
10. 11. 12.
deg: deg: deg:
coeff: coeff: coeff:
justify: justify: justify:
13. 14. 15.
deg: deg: deg:
coeff: coeff: coeff:
justify: justify: justify:
pf3
pf4

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Download Identify the leading coefficient, degree, and end behavior. 1 ... and more Study notes Pre-Calculus in PDF only on Docsity!

Math 3 Unit 3 Worksheet 1 Name:

End Behavior of Polynomial Functions Date: Per: ______

Identify the leading coefficient, degree, and end behavior.

2

2

3

2

Degree: Degree: Degree:

Leading Coeff: Leading Coeff: Leading Coeff:

End Behavior: End Behavior: End Behavior:

3

2

7

4

3

2

4

Degree: Degree: Degree:

Leading Coeff: Leading Coeff: Leading Coeff:

End Behavior: End Behavior: End Behavior:

Identify the end behavior. Justify your answer.

5

4

3

4

3

2

6

4

9

Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.

Justify your answer.

deg: deg: deg:

coeff: coeff: coeff:

justify: justify: justify:

deg: deg: deg:

coeff: coeff: coeff:

justify: justify: justify:

  1. Write a polynomial function with end behavior of:

on the left ๐‘“๐‘“(๐‘ฅ๐‘ฅ) goes to + โˆž and on the right ๐‘“๐‘“(๐‘ฅ๐‘ฅ) goes to โˆ’ โˆž.

  1. Write a polynomial function with end behavior of:

on the left ๐‘“๐‘“(๐‘ฅ๐‘ฅ) goes to + โˆž and on the right ๐‘“๐‘“(๐‘ฅ๐‘ฅ) goes to + โˆž.

  1. Sketch a graph of a polynomial function with

a negative lead coefficient and an even degree.

  1. Sketch a graph of a polynomial function with

a positive lead coefficient and an odd degree.

  1. The equation of the polynomial function to the right is

4

3

2

Write an equation for a translation

of ๐‘“๐‘“(๐‘ฅ๐‘ฅ) that has no ๐‘ฅ๐‘ฅ-intercepts.

(If not possible, explain why.)

  1. The equation of the polynomial function to the right is

3

2

Write an equation for a translation

of ๐‘”๐‘”(๐‘ฅ๐‘ฅ) that has no ๐‘ฅ๐‘ฅ-intercepts.

(If not possible, explain why.)

โˆ’4 โˆ’3 โˆ’2 โˆ’1 1 2 3 4 5

โˆ’

โˆ’

โˆ’

โˆ’

1

2

3

4

x

y

โˆ’4 โˆ’3 โˆ’2 โˆ’1 1 2 3 4 5

โˆ’

โˆ’

โˆ’

โˆ’

1

2

3

4

x

y