Polynomial Analysis Worksheets Grade 12

1. lim(x→∞) (4x⁵ - 3x⁴ + 7x² - 9)/(2x⁵ - 5x³ + 8) = ?
2. f(x) = -8x⁹ + 12x⁵ - 7x³ + 4. Describe the end behavior of f(x) as x → ∞ and as x → -∞.
3. Aroha is studying the long-term behavior of a polynomial function that models the profit (in thousands of dollars) of a company over time, where x represents the number of years since the company was founded. The profit function is P(x) = -7x^9 + 4x^5 - 2x^3 + 11. Describe the end behavior of this polynomial function as x approaches positive infinity and as x approaches negative infinity.

…and 5 more problems

1. f(x) = -5x⁷ + 20x³ - 15. Describe the end behavior as x → ∞ and x → -∞.
2. Kaia is sketching the graph of the polynomial function f(x) = -9x^8 + 14x^5 - 22x^2 + 7 on a coordinate plane. Describe the end behavior of this polynomial by completing the statements: As x → -∞, f(x) → ? and As x → +∞, f(x) → ?
3. lim(x→∞) (4x⁵ - 3x³ + 7x - 2)/(2x⁵ - x² + 5) = ?

…and 5 more problems

1. lim(x→∞) (3x⁴ - 2x³ + 5x - 1)/(2x⁴ + x² - 7) = ?
2. Sophia is studying the flight path of a model rocket. The height of the rocket above the ground, in meters, after t seconds is modeled by the polynomial function h(t) = -7t^4 + 9t^3 + 12t^2 + 5t. Describe the end behavior of this polynomial function as t approaches positive and negative infinity.
3. A polynomial function f(x) = 3x^5 - 2x^4 + 7x^2 - 5 is graphed on a coordinate plane. The graph shows the function approaching negative infinity as x approaches negative infinity, and approaching positive infinity as x approaches positive infinity. The function has exactly four real roots at x = -2, x = -1, x = 1, and x = 2, and the graph crosses the x-axis at all four roots. What is the degree of this polynomial?

…and 4 more problems