Characteristics of Polynomials Pre-AP

1. Sort the characteristics of the polynomial f(x) = x5 + 3x2 - 5x -2 Domain {x| x ∈ R} Range {y| y ∈ R} Increasing Intervals (-∞,-1.26) (0.67, ∞) Decreasing Intervals (-1.26, 0.67) Max on domain [-2,0] (-1.26, 5.89) Min on domain [0,2] (0.67, -3.87) x-intercepts -1.73 -0.33 1.28 y-intercept -2 Use the function f(x) = -x3 + x2 + 2x -1 for questions 2 - 10. 2. What is the domain of the function? (Use the function above) (-∞, 1] (-1, ∞) (-∞, ∞) [-1 , 1) 3. What is the range of the function? (-∞, -1] (1, ∞) (-∞, ∞) [-1 , 1) 4. What is (are) the x-intercept(s)? (Select all that apply) (-1.24,0) (0,-1) (0.45,0) (1.8,0) 5. What is (are) the y-intercept(s)? (Select all that apply) (-1.24,0) (0,-1) (0.45,0) (1.8,0) 6. What is the minimum on the domain [-2 , 1]? -2.1 1 -1.1 -1.6 7. What is the maximum on the domain [0,2]? -2.1 1.1 -1 1.6 8. What is the minimum on the domain [0,2] -1 -2.1 1.6 1.1 9. What is the domain the graph is increasing? Select all the apply. (-0.55, 1.21) (-∞, -0.55) (1.21, ∞) (-∞, ∞) 10. What is the domain the graph is decreasing? Select all the apply. (-0.55, 1.21) (-∞, -0.55) (1.21, ∞) (-∞, ∞) Use the function g(x) = 0.2x2(x + 1)(x + 5)3 for questions 11-14.11. State if the degree is even or odd and if they leading coefficient is positive or negative. Even Degree; positive leading coefficient Even Degree; negative leading coefficient Odd Degree; positive leading coefficient Odd Degree; negative leading coefficient 12. State the x-intercepts, multiplicities, and if the graph bounces or crosses at that x-intercept. x-intercept: 0 Multiplicity: 2 Bounce or Cross: Bouncex-intercept: -1 Multiplicity: 1 Bounce or Cross: Crossx-intercept: -5 Multiplicity: 3 Bounce or Cross: Cross 13. Describe the end behavior of the function. As x→-∞, f(x)→-∞As x→∞, f(x)→-∞ As x→-∞, f(x)→∞As x→∞, f(x)→∞ As x→-∞, f(x)→∞As x→∞, f(x)→-∞ As x→-∞, f(x)→-∞As x→∞, f(x)→∞ 14. Which graph represents the function? a b c d Use the function g(x) = -0.1(x + 1)(x+3)2(x - 3)4 for questions 15-18.15. State if the degree is even or odd and if they leading coefficient is positive or negative. Even Degree; positive leading coefficient Even Degree; negative leading coefficient Odd Degree; positive leading coefficient Odd Degree; negative leading coefficient 16. State the x-intercepts, multiplicities, and if the graph bounces or crosses at that x-intercept. x-intercept: -1 Multiplicity: 1 Bounce or Cross: Crossx-intercept: -3 Multiplicity: 2 Bounce or Cross: Bouncex-intercept: 3 Multiplicity: 4 Bounce or Cross: Bounce 17. Describe the end behavior of the function. As x→-∞, f(x)→-∞As x→∞, f(x)→-∞ As x→-∞, f(x)→∞As x→∞, f(x)→∞ As x→-∞, f(x)→∞As x→∞, f(x)→-∞ As x→-∞, f(x)→-∞As x→∞, f(x)→∞ 18. Which graph represents the function? a b c d Properties of Polynomials notes These are the same notes as in schoology.