Function End Behavior Worksheets Grade 12

1. A civil engineer is designing a suspension bridge where the cable's shape is modeled by the function f(x) = (4x³ - 3x² + 7)/(2x³ + 5x - 1), with x representing the horizontal distance from the center in meters. As the distance from the center increases indefinitely in either direction, what height does the cable approach above the roadway?
2. lim(x→∞) (3x⁵ - 2x³ + 7)/(4x⁵ - x² + 9) = ?
3. lim(x→∞) (4x⁵ - 2x³ + 8)/(3x⁵ + 5x² - 1) = ?

…and 5 more problems

1. lim(x→-∞) (8x⁶ - 6x⁴ + 2)/(4x⁶ + 10x³ - 2) = ?
2. Aroha, an environmental physicist, is modeling the rate of radioactive decay in a contaminated soil sample. The decay rate R(t) (in becquerels per kilogram) as a function of time t (in years) is given by R(t) = (9t^3 - 12t^2 + 15) / (3t^3 + 6t - 8). As time approaches infinity, what constant decay rate does the model approach?
3. Noah is an environmental scientist modeling the concentration of a pollutant in a river over time after a cleanup effort begins. The concentration C(t) in parts per million (ppm) is given by the function C(t) = (6t^2 - 11t + 1) / (t^2 + 6t - 1), where t represents time in months since the cleanup started. As t approaches infinity, what concentration level does the pollutant approach according to this model?

…and 4 more problems

1. lim(x→∞) (3x³ - 4x² + 2)/(2x³ + 5x - 1) = ?
2. Matiu is a marine biologist studying the population dynamics of a certain fish species in a large ocean ecosystem. He models the population size (in thousands) as a function of time t (in years) using the rational function P(t) = (5t^4 - 2t^3 + 7t + 11) / (10t^4 + 3t^2 - 8). As t approaches positive infinity, what population size (in thousands) does Matiu's model predict the fish population will approach?
3. Noah is a climate scientist studying the long-term concentration of a pollutant in a lake. The concentration C(t) in parts per million (ppm) is modeled by the rational function C(t) = (9t^2 - 7t + 12) / (3t^2 + 2t - 5), where t represents time in years. As t approaches positive infinity, what steady-state concentration does the pollutant approach according to this model? Express your answer as a simplified fraction or integer.

…and 4 more problems