Rational Functions Worksheets Grade 12

1. lim(x→∞) (4x³ - 2x² + 7)/(3x³ + 5x - 1) = ?
2. lim(x→∞) (5x³ - 2x² + 3x - 7)/(4x³ + x² - 5x + 2) = ?
3. lim(x→∞) (5x³ - 2x² + 3x - 1)/(4x³ + x² - 7) = ?

…and 3 more problems

1. An environmental engineer is modeling the population growth of an endangered species in a protected habitat. The population function is given by P(t) = (2t² + 5t - 3)/(t² - 9), where P(t) represents the population in hundreds and t represents years since the conservation program began. The conservation team needs to understand the long-term carrying capacity of the habitat and identify any critical time points where the population model becomes undefined. Determine all vertical and horizontal asymptotes of this population function.
2. A pharmaceutical company is modeling the concentration of a new medication in a patient's bloodstream over time using the function C(t) = (3t² + 5t) / (t² - 4), where C is concentration in mg/L and t is time in hours. The medical team needs to understand the long-term behavior of the drug concentration and identify any time points where the concentration becomes undefined. Determine the horizontal asymptote of this function and identify the vertical asymptotes.
3. An environmental engineer is modeling the rate of pollutant absorption in a wetland using the function R(x) = (2x² - 5x + 3)/(x² - 9), where R(x) represents the absorption rate in grams per square meter per day and x represents the distance from the pollution source in kilometers. The engineering team needs to understand the long-term absorption rate as distance increases and identify any distances where the absorption model becomes undefined. Determine all vertical and horizontal asymptotes of this absorption rate function.

…and 3 more problems

1. A pharmaceutical company is modeling the concentration of a new medication in a patient's bloodstream over time using the rational function C(t) = (3t² + 12t) / (t² + 4t + 3), where C(t) represents the concentration in milligrams per liter and t represents time in hours after administration. The researchers need to determine the long-term concentration level that the medication approaches and identify any times when the concentration becomes undefined due to vertical asymptotes. What is the horizontal asymptote representing the long-term concentration, and at what time values does the concentration become undefined?
2. A civil engineer is designing a suspension bridge where the cable shape follows the rational function f(x) = (2x² - 8x + 6)/(x² - 9), where x represents the horizontal distance from the center of the bridge in meters and f(x) represents the cable height above the roadway. To ensure proper clearance and structural integrity, the engineer needs to determine the cable's long-term behavior and identify any positions where the height becomes undefined. Find all vertical and horizontal asymptotes of this bridge cable function.
3. A pharmaceutical company 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 and C(t) is measured in milligrams per liter. The medical team needs to understand the long-term behavior of this medication to determine appropriate dosing intervals. What horizontal asymptote does this concentration function approach as time increases indefinitely?

…and 2 more problems