Identify any vertical, horizontal, or oblique asymptotes in the graph of y=ƒ(x). State the domain of ƒ.

Key Concepts

Asymptotes

Asymptotes are lines that a graph approaches but never touches. Vertical asymptotes occur where a function approaches infinity, typically at points where the function is undefined. Horizontal asymptotes indicate the behavior of a function as x approaches infinity or negative infinity, showing the value the function approaches. Oblique asymptotes occur when the function approaches a linear function as x approaches infinity.

Domain of a Function

The domain of a function is the set of all possible input values (x-values) for which the function is defined. It is crucial to identify any restrictions, such as values that lead to division by zero or negative square roots. Understanding the domain helps in analyzing the behavior of the function and its graph, particularly in relation to asymptotes.

Graph Interpretation

Interpreting a graph involves analyzing its features, such as intercepts, asymptotes, and overall shape. This skill is essential for understanding the behavior of the function represented. By examining the graph, one can identify vertical and horizontal asymptotes, as well as the general trend of the function, which aids in determining the domain and range.