Vertical Asymptotes

A vertical asymptote is a vertical line that a graph approaches but does not touch. It is a line on the graph where the function approaches positive or negative infinity as the input approaches a certain value.

To find the vertical asymptotes of a function, follow these steps:

1. Identify the values of the function's input that make the denominator of the function equal to zero. These are the potential values for vertical asymptotes.
2. Check if the function approaches positive or negative infinity as the input approaches each potential value. If the function approaches infinity, then there is a vertical asymptote at that value.

For example, consider the function f(x) = 1 / (x - 2). The denominator is equal to zero when x = 2. As x approaches 2 from the left, f(x) approaches negative infinity, and as x approaches 2 from the right, f(x) approaches positive infinity. Therefore, the function has a vertical asymptote at x = 2.

Here are some key points to remember about vertical asymptotes:

• A vertical asymptote can occur when the denominator of a function equals zero.
• The function approaches positive or negative infinity as the input approaches the vertical asymptote.
• Vertical asymptotes can be found by identifying the values that make the denominator equal to zero and determining the behavior of the function around those values.

It's important to note that not all functions have vertical asymptotes, and it's possible for a function to have multiple vertical asymptotes.

Practice identifying and understanding the behavior of functions around vertical asymptotes to strengthen your understanding of this concept.

Hope this helps!