Vertical and Horizontal Asymptotes
In this lesson, we will learn about vertical and horizontal asymptotes and their importance in graphing rational functions.
A vertical asymptote is a vertical line that the graph approaches but never touches. It usually occurs when the denominator of a rational function equals zero and the function becomes undefined. This means the function values increase or decrease without limit near this line.
A horizontal asymptote is a horizontal line that the graph approaches as x becomes very large or very small (positive or negative infinity). It describes the end behavior of the function and shows the value that the function gets closer to but does not necessarily reach.
Understanding vertical and horizontal asymptotes helps students analyze graphs, determine function behavior, and sketch graphs accurately.
By the end of this lesson, students will be able to identify vertical and horizontal asymptotes and use them to understand and draw rational functions correctly.