Practice Asymptote in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
An asymptote is a line that a curve approaches arbitrarily closely as the input (or output) grows without bound, but typically never reaches.
The graph gets infinitely close but never touches—like chasing something forever.
Example 1
easyFind the vertical and horizontal asymptotes of f(x) = \dfrac{3x}{x - 2}.
Example 2
hardFind the oblique (slant) asymptote of g(x) = \dfrac{x^2 + x - 1}{x - 1}.
Example 3
easyIdentify all asymptotes of h(x) = \dfrac{5}{x + 3}.
Example 4
mediumFor f(x) = \dfrac{2x^2 - 3}{x^2 + 1}, determine the horizontal asymptote and verify by computing f(100).