Name: Date: Math Unit 3 Worksheet 1 End Behavior of Polynomial Functions Per: ______ Identify the leading coefficient, degree, and end behavior. 1. 𝑓𝑓(𝑥𝑥) = 5𝑥𝑥 2 + 7𝑥𝑥 −3 2. 𝑦 𝑦 = −2𝑥𝑥 2 − 3𝑥 𝑥 + 4 3. 𝑔𝑔(𝑥𝑥) = 𝑥𝑥 3 − 9𝑥𝑥 2 + 2𝑥 𝑥 + 6 Degree: 3 Degree: 3 Degree: 6 Leading Coeff: + Leading Coeff: - Leading Coeff: + End Behavior: down down End Behavior: up up 4. 𝑦 𝑦 = −7𝑥𝑥 3 + 3𝑥𝑥 2 + 12𝑥𝑥 −1 End Behavior: down down 5. ℎ(𝑥𝑥) = −2𝑥𝑥 7 + 5𝑥𝑥 4 − 3𝑥𝑥 Degree: 6 Degree: 12 Leading Coeff: - Leading Coeff: End Behavior: End Behavior: up down 6. 𝑔𝑔(𝑥𝑥) = 8𝑥𝑥 3 + 4𝑥𝑥 2 + 7𝑥𝑥 4 − 9𝑥𝑥 Degree: 10 - Leading Coeff: End Behavior: up down + up up Identify the end behavior. Justify your answer. 7. 𝑓𝑓(𝑥𝑥) = 4𝑥𝑥 5 − 3𝑥𝑥 4 + 2𝑥𝑥 3 8. 𝑦 𝑦 = −𝑥𝑥4 + 𝑥𝑥 3 −𝑥𝑥 2 + 1 − 1 up down down down down up 9. ℎ(𝑥𝑥) = 3𝑥𝑥 6 − 7𝑥𝑥 4 − 2𝑥𝑥 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: odd deg: even deg: odd coeff: + coeff: - coeff: - justify: down up 13. deg: coeff: justify: justify: down down 14. even up up Math Unit 3 up down 15. odd deg: odd - coeff: - justify: up down justify: deg: coeff: + justify: down up turn turn down Worksheet 1 16. Write a polynomial function with end behavior of: on the left 𝑓𝑓(𝑥𝑥) goes to + ∞ and on the right 𝑓𝑓(𝑥𝑥) goes to − ∞ . -12x^3+9x+4 17. Write a polynomial function with end behavior of: on the left 𝑓𝑓(𝑥𝑥) goes to + ∞ and on the right 𝑓𝑓(𝑥𝑥) goes to + ∞ . 3x^2-13+7 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. y 20. The equation of the polynomial function to the right is 4 3 𝑓𝑓(𝑥𝑥) = 𝑥𝑥 4 + 𝑥𝑥 3 − 2𝑥𝑥 2 − 1 2 Write an equation for a translation of 𝑓𝑓(𝑥𝑥) that has no 𝑥𝑥-intercepts. (If not possible, explain why.) 1 x −4 −3 −2 −1 1 2 3 4 5 −1 −2 −3 −4 21. The equation of the polynomial function to the right is y 𝑔𝑔(𝑥𝑥) = −2𝑥𝑥 3 + 2𝑥𝑥 2 + 4𝑥𝑥 4 3 Write an equation for a translation of 𝑔𝑔(𝑥𝑥) that has no 𝑥𝑥-intercepts. (If not possible, explain why.) 2 1 x −4 −3 −2 −1 1 −1 −2 −3 −4 Math Unit 3 Worksheet 1 2 3 4 5 Determine the degree of the polynomial in factored form. Then demonstrate that you are correct by writing the polynomial in standard form. 22. 𝑦 𝑦 = (𝑥 𝑥 + 3)(𝑥𝑥 2 − 5𝑥𝑥 −4) degree 3 x^3-2x^2-19x-12 box method 23. 𝑦 𝑦 = 𝑥𝑥 3 (𝑥𝑥 −2)2 (𝑥 𝑥 + 1) degree 6 24. 𝑦 𝑦 = 𝑥𝑥(𝑥 𝑥 + 3)(𝑥𝑥 −1)2 degree 4 25. Describe in words how you can know the degree without multiplying out to write the polynomial in standard form. you can count the x in the parenthesis and the exponents outside the parenthesis Math Unit 3 Worksheet 1

End Behavior of Polynomial Functions

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