Asymptotes Worksheets Grade 12

1. Tane is a fluid dynamics engineer analyzing the flow rate of water through a filtration system. The flow rate over time is modeled by the function R(t) = (3t³ + 5t² - 7t + 9)/(t² - 5t + 6), where R(t) represents the flow rate in liters per minute and t represents time in hours. To understand the system's behavior at critical times and its long-term trend, Tane needs to determine all vertical and slant asymptotes of this function. What are the equations of these asymptotes?
2. A rational function is graphed on a coordinate plane with the equation f(x) = (3x² - 5x - 2)/(x² - 4). Describe all vertical and horizontal asymptotes of this function, providing their equations.
3. Find the vertical and horizontal asymptotes of f(x) = (4x² - 7x + 2)/(x² - 9) = ?

…and 5 more problems

1. Emma is an environmental engineer analyzing the concentration of a contaminant in a river over time. She models the concentration, C(t), in parts per million, using the rational function C(t) = (5t² + 20t - 15) / (t² - 25), where t represents the time in days since the start of monitoring. To understand the long-term behavior of the contaminant and identify days when the model breaks down, Emma needs to find all vertical and horizontal asymptotes of this function. What are the equations of these asymptotes?
2. lim(x→∞) (5x³ - 3x² + 2x - 7)/(2x³ + 4x² - x + 1) = ?
3. A biomedical engineer is modeling the concentration of a new medication in a patient's bloodstream over time. The concentration function is given by C(t) = (3t² + 5t - 2)/(t² - 4), where t represents hours after administration. To determine the long-term behavior of the medication concentration, the engineer needs to find all vertical and horizontal asymptotes of this function. What are the equations of these asymptotes?

…and 3 more problems

1. Sophia is a pharmacokineticist modeling the concentration of a new antibiotic in a patient's bloodstream. The concentration function is C(t) = (4t² - 7t + 2) / (t² - 11t + 28), where C(t) is in micrograms per milliliter and t is time in hours after the first dose. Determine all vertical and horizontal asymptotes of this function to understand critical time points and long-term drug behavior.
2. Mere is an astrophysicist analyzing the trajectory of a comet passing near a star. The comet's distance from the star (in millions of kilometers) over time t (in days) is modeled by the rational function D(t) = (4t³ - 11t + 6) / (t² - 25). To predict when the comet might approach dangerously close or escape the star's gravitational influence, Mere needs to find all vertical, horizontal, and slant asymptotes of this function. What are the equations of all asymptotes?
3. A biomedical engineer is modeling the concentration of a new medication in a patient's bloodstream using the function C(t) = (3t² + 5t - 2)/(t² - 4), where C(t) represents the concentration in milligrams per liter and t represents time in hours after administration. Determine all vertical and horizontal asymptotes of this function to understand the long-term behavior and critical time points of the medication concentration.

…and 3 more problems