Polynomial Analysis Worksheets Grade 12

1. lim(x→∞) (4x⁵ - 3x³ + 7x - 2)/(2x⁵ - 5x² + 9) = ?
2. Mere is analyzing the long-term behavior of a polynomial function that models the height in meters of a drone over time in hours. The function is f(x) = -6x^8 + 4x^3 - 2. Describe the end behavior of this polynomial as x approaches positive and negative infinity.
3. f(x) = -6x¹¹ + 21x⁶ - 4x³ + 1. Describe the end behavior as x → ∞ and x → -∞.

…and 4 more problems

1. lim(x→∞) (4x⁵ - 3x³ + 7x - 2)/(2x⁵ + 5x² - 9) = ?
2. Noah is analyzing the long-term behavior of a polynomial function that models the profit (in thousands of dollars) of a tech startup over time, where x represents years since the company's founding. The function is f(x) = 7x⁶ - 9x³ + 2x - 5. Describe the end behavior of this polynomial as x → ∞ and as x → -∞.
3. Charlotte is analyzing the long-term behavior of a polynomial function that models the growth of a certain biological population over time. The function is f(x) = -9x^7 + 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. Matiu is an environmental scientist modeling the population of a rare bird species in a protected forest. The population (in hundreds) over time t (in years) is modeled by the polynomial function P(t) = -2t⁶ + 4t⁴ - 6t² + 10. As time goes on (t → ∞) and as we look back in time (t → -∞), what happens to the bird population? Describe the end behavior of P(t) using the degree and leading coefficient.
2. Matiu is analyzing the graph of a polynomial function on a coordinate plane. The graph rises on the left side as x → -∞ and falls on the right side as x → +∞. The function is f(x) = -2x^6 + 4x^4 - 6x^2 + 8. Determine the degree of the polynomial and the sign of its leading coefficient.
3. lim(x→∞) (4x⁵ - 3x³ + 7x - 2)/(2x⁵ - x² + 5) = ?

…and 5 more problems