While vertical asymptotes describe the behavior of a graph as the output gets very large or very small, horizontal asymptotes help describe the behavior of a graph as the input gets very large or very small.

Jul 23, 2025 · Answer: To identify the vertical asymptotes of a function, set the denominator equal to zero and solve for x. Since the denominator is factored, set each factor equal to zero and solve …

Nov 14, 2025 · Vertical asymptotes typically occur at points where the function is undefined due to division by zero, and they correspond to non-removable discontinuities. Horizontal asymptotes …

An asymptote is a line to which the graph of a curve is very close but never touches it. There are three types of asymptotes: horizontal, vertical, and slant (oblique) asymptotes. Learn about each of them …

The following diagram shows the different types of asymptotes: horizontal asymptotes, vertical asymptotes, and oblique asymptotes. Scroll down the page for more examples and solutions on how …

It is a horizontal asymptote when: as x goes to infinity (or −infinity) the curve approaches some constant value b. It is a vertical asymptote when: as x approaches some constant value c (from the left or …

In this wiki, we will see how to determine horizontal and vertical asymptotes in the specific case of rational functions. (Functions written as fractions where the numerator and denominator are both …

The asymptotes most commonly encountered in the study of calculus are of curves of the form y = ƒ(x). These can be computed using limits and classified into horizontal, vertical and oblique asymptotes …

Functions don’t cross their vertical asymptotes, but they may cross their horizontal asymptotes. 1. Horizontal Asymptotes. A horizontal asymptote is an imaginary horizontal line on a graph. It shows …

An asymptote is a line that the graph of a function approaches. IMPORTANT: The graph of a function may cross a horizontal asymptote any number of times, but the graph continues to approach the …