Polynomial Function Review

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Presentation transcript:

Polynomial Function Review “ARE YOU READY FOR THIS?” Polynomial Function Review

Student will be able to identify polynomial functions by degree. 1. Classify this polynomial by degree: f(x) = 4x³ + 2x² - 3x + 7 a. binomial b. 4 term c. cubic d. quartic How do you know?

Student will be able to identify polynomial functions by degree. 2. Classify this polynomial by degree: f(x) =(x – 5i)(x + 5i) a. binomial b. quadratic c. cubic d. quartic How do you know?

Student will be able to identify polynomial functions by degree. 3. Classify the polynomial by degree if it has the following zeros: { 7, 1 mult. 2, -2} a. binomial b. 4 term c. cubic d. quartic How do you know?

Student will be able to identify polynomial functions by number of terms. 4.Classify this polynomial by number of terms: f(x) = -2x³ + 2x² - 3x + 7 a. trinomial b. 4 term c. cubic d. binomial How do you know?

Student will be able to put polynomial functions in standard form. 5. Put this polynomial in standard form: f(x) = -2x + 43 - 3x² + 7x⁵ a. f(x) = -2x + 43 - 3x² + 7x⁵ b. f(x) = 43 -2x + - 3x² + 7x⁵ c. f(x) = - 3x² -2x + 7x⁵ + 43 d. f(x) = 7x⁵ - 3x² -2x + 43 How do you know?

Student will be able to identify the leading coefficient of a polynomial function. 6. Identify the leading coefficient of this polynomial: f(x) = -2x³ + 2x² - 3x + 7 a. 7 b. -2x c. -2 d. x How do you know?

Student will be able to identify the leading coefficient of a polynomial function. 7. Identify the leading coefficient of this polynomial: f(x) = -x² + 2x³ - 3x + 7 a. -1 b. 7 c. 2 d. x How do you know?

Student will be able to identify the leading coefficient of a polynomial function. 8. Identify the leading coefficient of this polynomial: f(x) = -x³ + 4x² - 3x + 7 a. 7 b. -x³ c. 4 d. -1 How do you know?

Student will be able to identify the end behavior of a polynomial function. 9. Identify the end behavior of this polynomial: f(x) = -x³ + 4x² - 3x + 7 a. x -> -∞, y -> +∞ x -> +∞, y -> -∞ b. x -> -∞, y -> +∞ x -> +∞, y -> +∞ c. x -> -∞, y -> -∞ d. x -> -∞, y -> -∞ How do you know the right side? How do you know the left side?

Student will be able to write polynomial equations given real and/or complex roots. 10. Write the polynomial function with these roots in factored form: { 3 mult. 2, -4i } a. f(x) = (x - 2)(x - 2)(x – 2)(x + 4i) b. f(x) = (x - 3)(x - 3)(x + 4i)(x – 4i) c. f(x) = (x + 3)(x + 3)(x + 4i)(x – 4i) d. f(x) = (x - 2)(x - 2)(x – 2)(x + 4i)(x – 4i) How do you know?

Student will be able to write polynomial equations given real and/or complex roots. 11. Write the polynomial function with these factors in standard form: (x – 2)(x + 1)(x – 1) a. f(x) = x³ - x² + x - 2 b. f(x) = x³ - x² + x + 2 c. f(x) = x³ - 2x² + x - 2 d. f(x) = x³ - 2x² - x + 2 How do you know?

Student will be able to graph polynomial functions. 12. Identify the y-intercept of this polynomial function: f(x) = 3x⁵ - 2x³ + 17 a. 3 b. 5 c. There is no y-intercept d. 17 How do you know?

Student will be able to graph polynomial functions. 13. Identify the y-intercept of this polynomial function: f(x) = -6x⁵ - 12x³ + 17x a. -6 b. 0 c. There is no y-intercept d. 17 How do you know?

Student will be able to divide polynomials with synthetic division. 14. Choose the correct way to set up a Synthetic Division of this polynomial: 3x⁴ + 5x³ - 2x + 3 - x⁵ x - 3 a. -3 3 5 -2 3 -1 b. -3 -1 3 5 0 -2 3 c. 3 3 5 -2 3 -1 d. 3 -1 3 5 0 -2 3 Now solve it!

Student will be able to evaluate functions with synthetic division. 15. Evaluate f(4) if f(x) = 7x⁴ + 5x³ - 2x + 3 - x⁵ (Use synthetic division) a. f(4) = 2507 b. f(4) = 452 c. f(4) = 1083 d. f(4) = 2578 How do you know?

Student will be able to use graphing technology to find solutions for polynomial equations. 16. Use a graphing calculator to find the zeros of this polynomial function: f(x) = -4x³ + x² - 3 a. -3 b. -8 c. -.83 d. 5i How do you know?

Student will be able to use graphing technology to find solutions for polynomial equations. 17. Use a graphing calculator to find the relative extrema of this polynomial function: f(x) = -4x³ + x² - 3 a. relative maximum at (-1, -3) b. relative minimum and maximum at (.6, -3.6) c. relative maximum at (2, -4) d. relative minimum at (3, -.6) How do you know?

Student will be able to use graphing technology to find solutions for polynomial equations. 18. Use a graphing calculator to find the y value of this polynomial function where x = 5: f(x) = -4x³ + x² - 3 a. -3 b. -478 c. -5 d. 3 How do you know?

Students will be able to describe the roots of polynomial functions. 19. How many roots does this polynomial have? f(x) = 56x⁴ - 12x³ + 4x² - 3x + 1 a. 56 b. 1 c. 4 d. 5 How do you know?

Students will be able to describe the roots of polynomial functions. 20. What are the possible rational roots of this polynomial? f(x) = 6x⁴ - 12x³ + 4x² - 3x + 8 a. { ±8, ±6} b. {± 1, ± 2, ±4, ± 8, ±1/6, ±1/2, ±1/3, ±2/3, ±4/3, ±8/3} c. {± 1, ± 2, ±4, ± 6,± 8} d. {1, 2, 4, 8, 1/6, 1/2, 1/3, 2/3, 4/3, 8/3} How do you know?