Asymptotes Worksheets Grade 12

1. Find the horizontal asymptote of the function f(x) = (4x^3 - 2x^2 + 7)/(5x^3 + 3x - 1) as x approaches infinity. Enter the y-value only.
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. f(x) = (7x² + 2x - 7)/(x² - 7x + 12). Find all asymptotes.

…and 4 more problems

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

1. f(x) = (3x³ + 7x² - 5x + 1)/(x² - 9). Find all asymptotes.
2. Emma is a civil engineer designing a new highway. The project's daily cost (in thousands of dollars) is modeled by the rational function C(t) = (3t³ - 5t + 1) / (t² - 9), where t represents the number of months since construction began. To understand the project's long-term financial trajectory and identify critical months when the cost model becomes undefined, Emma must find all vertical and horizontal or slant (oblique) asymptotes of this function. What are the equations of all asymptotes?
3. A biomedical engineer is modeling the concentration of a new drug in a patient's bloodstream using the function C(t) = (5t² + 3t - 2)/(t² - 4), where t represents hours after administration. To ensure safe dosage levels, she needs to identify all vertical and horizontal asymptotes of this concentration function. What are the equations of these asymptotes?

…and 3 more problems