polynomial function review
DESCRIPTION
“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?. - PowerPoint PPT PresentationTRANSCRIPT
Polynomial Function Review
“ARE YOU READY FOR THIS?”
Student will be able to identify polynomial functions by degree.
1. Classify this polynomial by degree:f(x) = 4x³ + 2x² - 3x + 7
a. binomialb. 4 termc. cubicd. 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. binomialb. quadraticc. cubicd. 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. binomialb. 4 termc. cubicd. 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 + 7a. trinomialb. 4 termc. cubicd. 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 + 7x⁵b. f(x) = 43 -2x + - 3x² + 7x⁵c. f(x) = - 3x² -2x + 7x⁵ + 43d. 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 + 7a. 7b. -2xc. -2d. 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 + 7a. -1b. 7c. 2d. 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 + 7a. 7b. -x³c. 4d. -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 + 7a. x -> -∞, y -> +∞ x -> +∞, y -> -∞
b. x -> -∞, y -> +∞ x -> +∞, y -> +∞
c. x -> -∞, y -> -∞ x -> +∞, y -> -∞
d. x -> -∞, y -> -∞ 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 - 2b. f(x) = x³ - x² + x + 2c. f(x) = x³ - 2x² + x - 2d. 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. 3b. 5c. There is no y-interceptd. 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. -6b. 0c. There is no y-interceptd. 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 - 3a. -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. -3b. -8c. -.83d. 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. -3b. -478c. -5d. 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. 56b. 1c. 4d. 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?