Identifying Asymptotes in Functions

This lesson teaches how to identify asymptotes by examining functions. It begins with a review of the domain of a function, explaining that the domain is all real numbers except where the function is undefined, such as division by zero. The concept of an asymptote is introduced as a line that a graph approaches but never touches. The lesson uses the equation y = 1/x to illustrate a vertical asymptote at x = 0. It further explores the C of t function, showing how asymptotes appear when t = 0. The lesson concludes by addressing common misconceptions, emphasizing that a graph alone is insufficient to identify asymptotes.

What is the definition of a domain in the context of a function?

Explain why the domain of the function discussed in the lesson is all real numbers except for 0.

What is an asymptote and how is it represented in a graph?

Describe the significance of the vertical asymptote at x equals 0 in the context of the function y equals 1 over x.

How does the concept of asymptotes apply to the C of t function discussed in the lesson?

What misunderstanding about asymptotes is highlighted in the lesson?

Based on the graph of y equals 2 to the x, explain why there is no vertical asymptote at x equals 4.