math 3 unit 3: polynomial functions - cusd.com
TRANSCRIPT
Math 3 Unit 3: Polynomial Functions
Unit Title Standards
3.1 End Behavior of Polynomial Functions F.IF.7c
3.2 Graphing Polynomial Functions F.IF.7c, A.APR3
3.3 Writing Equations of Polynomial Functions F.IF.7c
3.4 Factoring and Graphing Polynomial Functions F.IF.7c, F.IF.8a, A.APR3
3.5 Factoring By Grouping F.IF.7c, F.IF.8a, A.APR3
3.6 Factoring By Division F.IF.7c, F.IF.8a, A.APR2, A.APR3, A.APR.6
Unit 3 Review
Additional Clovis Unified Resources http://mathhelp.cusd.com/courses/math-3 Clovis Unified is dedicated to helping you be successful in Math 3. On the website above you will find videos from Clovis Unified teachers on lessons, homework, and reviews. Digital copies of the worksheets, as well as hyperlinks to the videos listed on the back are also available at this site.
Math 3 Unit 3: Online Resources
3.1 End Behavior of Polynomial Functions
β’ Khan Academy: Intro to End Behavior of Polynomials http://bit.ly/31ebb
β’ Khan Academy: End Behavior of Functions & their Graphs http://bit.ly/31ebc
β’ Khan Academy: Article - End Behavior of Polynomials http://bit.ly/31ebd
β’ Purple Math: End Behavior http://bit.ly/31ebp
β’ Yay Math: Polynomial Functions http://bit.ly/31ebg
3.2 Graphing Polynomial Functions
β’ Math is Fun: Solving Polynomials http://bit.ly/32gpfa
β’ Purple Math: Degrees, Turnings, and "Bumps" http://bit.ly/32gpfb
β’ Purple Math: Zeroes and their Multiplicities http://bit.ly/32gpfc
β’ Purple Math: Quickie Graphing of Polynomials http://bit.ly/32gpfe
β’ Khan Academy: Zeros of Polynomials & their Graphs http://bit.ly/32gpff
β’ Khan Academy: Article - Graphs of Polynomials http://bit.ly/32gpfg
β’ Graphing a Polynomial Function in Factored Form β’ http://bit.ly/32gpfh and http://bit.ly/32gpfi
3.3 Writing Equations of Polynomial Functions
β’ How to Write the Equation of a Polynomial Function from its Graph http://bit.ly/33wepfa
β’ Purple Math: More about Zeros and their Multiplicities (see example 3) http://bit.ly/33wepfb
3.4 Factoring & Graphing Polynomials
β’ She Loves Math: Graphing and Finding Roots of Polynomial Functions http://bit.ly/34fgpb
β’ Graphing Polynomial Functions by Factoring http://bit.ly/34fgpc
3.5 Factoring By Grouping
β’ Khan Academy: Factoring and Graphing Polynomial Equations by Grouping http://bit.ly/35fga
β’ Khan Academy: Zeros of Polynomials & their Graphs http://bit.ly/35fgb
3.6 Factoring By Division
β’ Zeros of a Polynomial Function by Factoring, Graphing, and Synthetic Division http://bit.ly/36fda
β’ Patrick JMT: Long Division of Polynomials http://bit.ly/36fdb
β’ Cool Math: Long Division with Polynomials http://bit.ly/36fdd
β’ Patrick JMT: Finding all the Zeros of a Polynomial β Synthetic Division http://bit.ly/36fdi and http://bit.ly/36fdj
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. ππ(π₯π₯) = 5π₯π₯2 + 7π₯π₯ β 3 2. π¦π¦ = β2π₯π₯2 β 3π₯π₯ + 4 3. ππ(π₯π₯) = π₯π₯3 β 9π₯π₯2 + 2π₯π₯ + 6 Degree: Degree: Degree:
Leading Coeff: Leading Coeff: Leading Coeff:
End Behavior: End Behavior: End Behavior: 4. π¦π¦ = β7π₯π₯3 + 3π₯π₯2 + 12π₯π₯ β 1 5. β(π₯π₯) = β2π₯π₯7 + 5π₯π₯4 β 3π₯π₯ 6. ππ(π₯π₯) = 8π₯π₯3 + 4π₯π₯2 + 7π₯π₯4 β 9π₯π₯ Degree: Degree: Degree:
Leading Coeff: Leading Coeff: Leading Coeff:
End Behavior: End Behavior: End Behavior: Identify the end behavior. Justify your answer.
7. ππ(π₯π₯) = 4π₯π₯5 β 3π₯π₯4 + 2π₯π₯3 8. π¦π¦ = βπ₯π₯4 + π₯π₯3 β π₯π₯2 + 1 β 1 9. β(π₯π₯) = 3π₯π₯6 β 7π₯π₯4 β 2π₯π₯9 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:
Math 3 Unit 3 Worksheet 1
16. Write a polynomial function with end behavior of: on the left ππ(π₯π₯) goes to + β and on the right ππ(π₯π₯) goes to β β .
17. Write a polynomial function with end behavior of:
on the left ππ(π₯π₯) goes to + β and on the right ππ(π₯π₯) goes to + β . 18. Sketch a graph of a polynomial function with a negative lead coefficient and an even degree. 19. Sketch a graph of a polynomial function with a positive lead coefficient and an odd degree. 20. The equation of the polynomial function to the right is ππ(π₯π₯) = π₯π₯4 + π₯π₯3 β 2π₯π₯2 β 1 Write an equation for a translation of ππ(π₯π₯) that has no π₯π₯-intercepts. (If not possible, explain why.) 21. The equation of the polynomial function to the right is ππ(π₯π₯) = β2π₯π₯3 + 2π₯π₯2 + 4π₯π₯ Write an equation for a translation of ππ(π₯π₯) that has no π₯π₯-intercepts. (If not possible, explain why.)
β4 β3 β2 β1 1 2 3 4 5
β4
β3
β2
β1
1
2
3
4
x
y
β4 β3 β2 β1 1 2 3 4 5
β4
β3
β2
β1
1
2
3
4
x
y
Math 3 Unit 3 Worksheet 1
Determine the degree of the polynomial in factored form. Then demonstrate that you are correct by writing the polynomial in standard form. 22. π¦π¦ = (π₯π₯ + 3)(π₯π₯2 β 5π₯π₯ β 4) 23. π¦π¦ = π₯π₯3(π₯π₯ β 2)2(π₯π₯ + 1) 24. π¦π¦ = π₯π₯(π₯π₯ + 3)(π₯π₯ β 1)2
25. Describe in words how you can know the degree without multiplying out to write the polynomial in standard form.
Math 3 Unit 3 Worksheet 1
Math 3 Unit 3 Worksheet 2
Math 3 Unit 3 Worksheet 2 Name: Graphing Polynomial Functions Date: Per: ______ For the functions below, identify each of the listed characteristics.
1. π¦π¦ = (π₯π₯ β 2)(π₯π₯ + 5)(π₯π₯ β 1) 2. ππ(π₯π₯) = π₯π₯2(π₯π₯ + 2)(π₯π₯ β 7)
a) degree & leading coefficient a) degree & leading coefficient
b) end behavior b) end behavior
c) π₯π₯-intercepts with multiplicity c) π₯π₯-intercepts with multiplicity
d) π¦π¦-intercept d) π¦π¦-intercept
e) How many distinct π₯π₯-intercepts? e) How many distinct π₯π₯-intercepts?
f) How many roots are there? f) How many zeros are there? Sketch graphs of the polynomial functions. Label all π₯π₯ and π¦π¦ intercepts.
3. π¦π¦ = (π₯π₯ β 1)(π₯π₯ + 3)(π₯π₯ β 4) 4. ππ(π₯π₯) = 2(π₯π₯ + 4)2(π₯π₯ β 2) 5. ππ(π₯π₯) = βπ₯π₯2(π₯π₯ β 3) 6. ππ(π₯π₯) = β3(π₯π₯ + 1)(π₯π₯ + 2)(π₯π₯ β 4)
Math 3 Unit 3 Worksheet 2
7. π¦π¦ = π₯π₯2(π₯π₯ + 5)(π₯π₯ β 3) 8. β(π₯π₯) = β(π₯π₯ + 2)(π₯π₯ β 3)2(π₯π₯ β 1) 9. ππ(π₯π₯) = 2(π₯π₯ + 4)(π₯π₯ + 2)(2 β π₯π₯)(π₯π₯ β 1) 10. ππ(π₯π₯) = β5π₯π₯2(π₯π₯ + 3)2 Given ππ(π₯π₯) = (π₯π₯ + 1)(π₯π₯ β 2)2. Sketch the following functions and label the indicated points.
11. Sketch π¦π¦ = ππ(π₯π₯) 12. Sketch π¦π¦ = ππ(π₯π₯) + 3 π₯π₯ and π¦π¦ intercepts relative minimums and π¦π¦ intercept
13. Sketch π¦π¦ = ππ(π₯π₯ + 3) 14. π¦π¦ = βππ(π₯π₯)
π₯π₯ intercepts and relative minimums π₯π₯ and π¦π¦ intercepts
Math 3 Unit 3 Worksheet 3
Math 3 Unit 3 Worksheet 3 Name: Writing Equations of Polynomial Functions Date: Per: ______ For #1-2, write an equation for the polynomial graph shown and determine if the leading coefficient, ππ, is + or β. 1. 2. For #3-4, write the equation for the polynomial graph shown with the lowest possible degree.
3. 4. Sketch the polynomial function containing the given points and write the equation. 5. Cubic 6. Quartic
(β7, 0); (β4, 0); (0, 7); (3, 0) (β6, 0); (β2, 0); (0,β20); (4, 0); (5, 0)
2 1 β1
β3
2 1
(β1,β12)
1 β1 β3 β2 3
Math 3 Unit 3 Worksheet 3
7. Sketch three different quartic functions which contain the given points: (β7, 0); (β4, 0); (0, 5); (3, 0) 8. Sketch a graph and write the equation of a quartic function whose graph
passes through (0,β2) and is tangent to the x-axis at (β1, 0) and (2, 0). 9. Sketch and write an equation of a polynomial that has the following characteristics: crosses the π₯π₯-axis only at β2 and 4, touches the π₯π₯-axis at 0 and 2, and is above the π₯π₯-axis between 2 and 4. 10. ππ(π₯π₯) is a cubic polynomial such that ππ(β3) = ππ(β1) = ππ(2) = 0 and ππ(0) = β6.
Sketch ππ(π₯π₯) and write its function. 11. If ππ(π₯π₯) is a cubic polynomial such that ππ(0) = 0, ππ(2) = β4, and ππ(π₯π₯) is above the π₯π₯-axis only when π₯π₯ > 4. Sketch ππ(π₯π₯) and write its function. 12. Answer the following statements as true or false regarding the graph
of the cubic polynomial function: ππ(π₯π₯) = πππ₯π₯3 + πππ₯π₯2 + πππ₯π₯ + ππ
a) It intersects the π¦π¦-axis in one and only one point. b) It intersects the π₯π₯-axis in at most three points. c) It intersects the π₯π₯-axis at least once. d) It contains the origin. e) The ends of the graph will both be going in the same direction.
Math 3 Unit 3 Worksheet 4
Math 3 Unit 3 Worksheet 4 Name: Factoring and Graphing Polynomial Functions Date: Per: ______ [1-6] Completely factor the following polynomials.
1. π₯π₯4 β 7π₯π₯2 + 10 2. π₯π₯4 β 15π₯π₯2 β 16 3. π₯π₯4 β 10π₯π₯2 + 9 4. π₯π₯4 β 25π₯π₯2 5. β2π₯π₯3 + 2π₯π₯ 6. βπ₯π₯3 + 9π₯π₯ [7-10] Factor, then sketch graphs of the polynomial functions. Label all π₯π₯- and π¦π¦-intercepts.
7. π¦π¦ = π₯π₯3 β 16π₯π₯ 8. π¦π¦ = (ππ β ππ)(π₯π₯) if ππ(π₯π₯) = π₯π₯ and ππ(π₯π₯) = β3π₯π₯2 + 12 9. π¦π¦ = π₯π₯4 β 10π₯π₯2 + 9 10. π¦π¦ = (ππ β ππ)(π₯π₯) if ππ(π₯π₯) = 2π₯π₯ and ππ(π₯π₯) = 2π₯π₯3 β 50π₯π₯
Math 3 Unit 3 Worksheet 4
[11-14] Factor each polynomial function, then sketch (labeling π₯π₯ and π¦π¦ intercepts) and answer the questions.
11. π¦π¦ = (ππ β ππ)(π₯π₯) if 12. β(π₯π₯) = βπ₯π₯4 β 4π₯π₯3 β 4π₯π₯2 ππ(π₯π₯) = 2π₯π₯3 and ππ(π₯π₯) = 12π₯π₯2 β 18π₯π₯ a) How many π₯π₯-intercepts? a) How many π₯π₯-intercepts? b) How many relative maximums? b) How many relative maximums? c) How many relative minimums? c) How many relative minimums? 13. ππ(π₯π₯) = βπ₯π₯3 + 3π₯π₯2 + 4π₯π₯ 14. ππ(π₯π₯) = β5π₯π₯4 β 10π₯π₯3 + 75π₯π₯2 a) How many π₯π₯-intercepts? a) How many π₯π₯-intercepts? b) How many relative maximums? b) How many relative maximums? c) How many relative minimums? c) How many relative minimums?
Math 3 Unit 3 Worksheet 5
Math 3 Unit 3 Worksheet 5 Name: Factoring by Grouping Date: ___________________Per:________ Factor completely over the integers:
1. π₯π₯(π₯π₯ + 2) + 3(π₯π₯ + 2) 2. π₯π₯(π₯π₯2 + 5) β 9(π₯π₯2 + 5) 3. π₯π₯2(π₯π₯ β 7) β 4(π₯π₯ β 7) 4. π₯π₯(π₯π₯2 + 3) β (3 + π₯π₯2) 5. 3π₯π₯(π₯π₯ β 2) β (2 β π₯π₯) 6. ππ(ππ + π π ) β ππ(ππ + π π ) + ππ(ππ + π π ) 7. ππ(π¦π¦ β 1) β ππ(1 β π¦π¦) 8. 9(2ππ β ππ) + π₯π₯2(ππ β 2ππ) 9. ππππ + ππππ + ππππ + ππππ 10. 5π₯π₯ β 5 + π₯π₯2 β π₯π₯3 11. 2π₯π₯3 β 10π₯π₯2 β 2π₯π₯ + 10 12. 3π€π€3 β 3π€π€2π§π§ + 18π€π€2 β 18π€π€π§π§ 13. 7ππ3 β 28ππ2 + 12 β 3ππ 14. 12 β 28π₯π₯ β 3π₯π₯2 + 7π₯π₯3 15. 4π₯π₯5 β π₯π₯3 + 8π₯π₯2 β 2 16. ππ3π₯π₯ + ππ2π₯π₯3 + ππ + π₯π₯2
Math 3 Unit 3 Worksheet 5
Factor and sketch the polynomial functions. Label π₯π₯ and π¦π¦ intercepts.
17. π¦π¦ = π₯π₯3 + 4π₯π₯2 β 4π₯π₯ β 16 18. ππ(π₯π₯) = 3π₯π₯3 + 9π₯π₯2 β 27π₯π₯ β 81
19. π¦π¦ = (ππ β ππ)(π₯π₯) if 20. π¦π¦ = ππ(π₯π₯) β ππ(π₯π₯) if ππ(π₯π₯) = π₯π₯4 + π₯π₯3 and ππ(π₯π₯) = 16π₯π₯2 + 16π₯π₯ ππ(π₯π₯) = 4π₯π₯4 + 8π₯π₯3 and ππ(π₯π₯) = 16π₯π₯2 + 32π₯π₯
Math 3 Unit 3 Worksheet 6
Math 3 Unit 3 Worksheet 6 Name: Factoring by Division Date: ___________________Per:________
Divide using polynomial long division:
1. (π₯π₯2 + 5π₯π₯ β 14) Γ· (π₯π₯ β 2) 2. (π₯π₯2 β 2π₯π₯ β 48) Γ· (π₯π₯ + 5) Is (π₯π₯ β 2) a factor of (π₯π₯2 + 5π₯π₯ β 14) ? Is (π₯π₯ + 5) a factor of (π₯π₯2 β 2π₯π₯ β 48) ? 3. (π₯π₯2 + 7π₯π₯ + 12) Γ· (π₯π₯ + 4) 4. (π₯π₯3 β 3π₯π₯2 + 8π₯π₯ β 6) Γ· (π₯π₯ β 1) Is (π₯π₯ + 4) a factor of (π₯π₯2 + 7π₯π₯ + 12)? Is (π₯π₯ β 1) a factor of (π₯π₯3 β 3π₯π₯2 + 8π₯π₯ β 6)? Divide using synthetic division:
5. (π₯π₯2 + π₯π₯ + 30) Γ· (π₯π₯ + 3) 6. (π₯π₯2 β 2π₯π₯ β 10) Γ· (π₯π₯ + 5) Is (π₯π₯ + 3) a factor of (π₯π₯2 + π₯π₯ + 30)? Is (π₯π₯ + 5) a factor of (π₯π₯2 β 2π₯π₯ β 10)? 7. (π₯π₯3 β 3π₯π₯2 β 16π₯π₯ β 12) Γ· (π₯π₯ β 6) 8. (π₯π₯4 β 7π₯π₯2 β 18) Γ· (π₯π₯ + 3) Is (π₯π₯ β 6) a factor of (π₯π₯3 β 3π₯π₯2 β 16π₯π₯ β 12)? Is (π₯π₯ + 3) a factor of (π₯π₯4 β 7π₯π₯2 β 18)?
Math 3 Unit 3 Worksheet 6
A polynomial ππ(π₯π₯) and a factor of ππ(π₯π₯) are given. Factor ππ(π₯π₯) completely.
9. ππ(π₯π₯) = π₯π₯3 β 12π₯π₯2 + 12π₯π₯ + 80 ; π₯π₯ β 10 10. ππ(π₯π₯) = π₯π₯3 β π₯π₯2 β 21π₯π₯ + 45 ; π₯π₯ + 5 Given one zero, factor and sketch the polynomial functions. Label π₯π₯ and π¦π¦ intercepts.
11. π¦π¦ = 2π₯π₯3 + 3π₯π₯2 β 39π₯π₯ β 20 ; 4 12. π¦π¦ = π₯π₯3 β π₯π₯2 β 8π₯π₯ + 12 ; β3
Math 3 Unit 3 Worksheet 6
13. a) Divide ππ(π₯π₯) by (π₯π₯ β 3) by the method of your choice: b) What was the remainder? ______
ππ(π₯π₯) = π₯π₯2 β 11π₯π₯ + 24
c) Find the value of ππ(3). ππ(3) =______________
14. a) Divide ππ(π₯π₯) by (π₯π₯ + 1) using the method of your choice: b) What was the remainder? ______
ππ(π₯π₯) = π₯π₯3 β π₯π₯2 + 2π₯π₯ + 7
c) Find the value of ππ(β1) ππ(β1) =______________
15. What pattern do you notice in the answers for # 13 and 14? 16. Based on your observations in problem 15, do you think (π₯π₯ β 1) will be a factor of (π₯π₯13 β 2π₯π₯ + 1)?
Math 3 Unit 3 Worksheet 6
Math 3 Unit 3 Review Worksheet
Math 3 Unit 3 Name: Review Worksheet Date: ___________________Per:________
Directions: Show valid, appropriate, & legible work.
[1-6]: For each of the following functions: (a) Determine the end behavior. (b) What is the π¦π¦-intercept? (c) Sketch a basic graph only indicating the general shape.
1) ππ(π₯π₯) = 5π₯π₯3 β 7π₯π₯2 β 2π₯π₯ + 1 2) ππ(π₯π₯) = β 2π₯π₯4 + 9π₯π₯3 β π₯π₯2 + π₯π₯ β 8 3) β(π₯π₯) = 4π₯π₯4 + 3π₯π₯3 + 2π₯π₯2 + π₯π₯
4) π¦π¦ = β 10π₯π₯3 + 3π₯π₯2 β 2π₯π₯ β 11 5) ππ(π₯π₯) = 2(π₯π₯ β 3)(π₯π₯ + 2)2(π₯π₯ β 5) 6) ππ(π₯π₯) = 1
3(6 β π₯π₯)(π₯π₯ + 2)3
Use the terms βdegreeβ and βlead coefficientβ to generalize the rules for determining end behavior. [7-8]: Looking back at #5 & #6 β¦
7) How many roots (zeros) does #5 have? ____ How many π₯π₯-intercepts does #5 have? ____ 8) How many zeros (roots) does #6 have? ____ How many π₯π₯-intercepts does #6 have? ____ [9-16]: (a) Write each function in completely factored form (over the integers). (b) Find all of the roots (real and imaginary) with their multiplicity, if different from 1. (c) How many π₯π₯-intercepts does the function have?
9) ππ(π₯π₯) = 4π₯π₯3 + 20π₯π₯2 β 9π₯π₯ β 45 10) ππ(π₯π₯) = π₯π₯5 β 50π₯π₯3 + 49π₯π₯ 11) π¦π¦ = π₯π₯3 β 4π₯π₯2 β 12π₯π₯ 12) ππ(π₯π₯) = π₯π₯3 β 12π₯π₯2 + 41π₯π₯ β 42 if (π₯π₯ β 7) is a factor of ππ.
x
y
x
y
x
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x
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x
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Math 3 Unit 3 Review Worksheet
13) ππ(π₯π₯) = 2π₯π₯3 + 3π₯π₯2 β 89π₯π₯ + 120 14) ππ(π₯π₯) = π₯π₯4 + 9π₯π₯2 β 36 if one of the roots is 5. 15) ππ(π₯π₯) = π₯π₯3 + 7π₯π₯2 + 34π₯π₯ + 66 16) π¦π¦ = 3π₯π₯4 β 16π₯π₯3 + 3π₯π₯2 + 46π₯π₯ + 24 if (π₯π₯ + 3) is a factor of ππ. if two of the zeros are β 1 and 4. [17-21]: Sketch the graph for each of the following; label π₯π₯- and π¦π¦-intercepts. {Hint: Finish factoring each first.}
17) π¦π¦ = π₯π₯(π₯π₯ + 3)2(2 β π₯π₯) 18) π¦π¦ = π₯π₯3 β π₯π₯2 β 2π₯π₯ 19) ππ(π₯π₯) = (π₯π₯2 β 3π₯π₯ β 4)(π₯π₯ β 4)
20) ππ(π₯π₯) = (π₯π₯2 + 2π₯π₯ β 3)(π₯π₯2 β 3π₯π₯ β 18) 21) β(π₯π₯) = (6 β 5π₯π₯ β π₯π₯2)(π₯π₯2 + 3π₯π₯ β 4)
22) Write an equation for the graph below: 23) Write the equation for the graph below:
-3 4
π¦π¦
π₯π₯
π¦π¦
π₯π₯
3
1 2 β1
Math 3 Unit 3 Review Worksheet
[24-27]: Write the equation for a polynomial function, given:
24) 6th degree polynomial with roots = οΏ½0 ππππππππ. 3, 52
, 3 ππππππππ. 2 οΏ½ and ππ(1) = 36. 25) 4th degree polynomial with zeros = οΏ½2 ππππππππ. 3,β3
4 οΏ½ and π¦π¦-intercept is 48.
26) Cubic polynomial with roots = {β4 ππππππππ. 2, 3} and ππ(1) = β20. 27) Write two different equations for a cubic polynomial, ππ(π₯π₯), that has only two distinct zeros, β1 and 2, and
ππ(1) = β4. 28) True/False a) It is possible for a cubic polynomial function with real coefficients to have all imaginary roots. b) It is possible for a 4th degree polynomial function with real coefficients to have all imaginary zeros. c) If βππβ is a root (zero) of the polynomial function ππ(π₯π₯), then (π₯π₯ β ππ) is a factor of ππ(π₯π₯). d) A polynomial function of degree βππβ has βππβ roots (zeros). e) A polynomial function of degree βππβ has βππβ π₯π₯-intercepts. [29-30]: (a) Find all of the zeros (roots) for each. (b) How many π₯π₯-intercepts does the function have?
29) ππ(π₯π₯) = π₯π₯4 + π₯π₯2 β 20 30) ππ(π₯π₯) = π₯π₯3 + 4π₯π₯2 β 9π₯π₯ β 36
Math 3 Unit 3 Review Worksheet
[31-38]: Given the graph of ππ(π₯π₯) with the five key labeled points. Describe the transformation in words, then sketch each transformation and label the 5 key points (π₯π₯, π¦π¦).
31) ππ(π₯π₯ + 5) 32) ππ(π₯π₯ β 2) Describe the translation: Describe the translation:
x
y
(0, 0) (2, 0)
(5, 0)
(1,β4)
(4, 8)
π¦π¦ = ππ(π₯π₯)
Math 3 Unit 3 Review Worksheet
33) ππ(π₯π₯) + 4 34) ππ(π₯π₯) β 8 Describe the translation: Describe the translation:
35) β ππ(π₯π₯) β 4 36) β ππ(π₯π₯) + 8 Describe the translation: Describe the translation:
37) ππ(π₯π₯ + 1) β 4 38) ππ(π₯π₯ β 3) + 5
Describe the translation: Describe the translation: