Use the graph of the rational function in the figure shown to complete each statement in Exercises 9–14.
As x -> 1^-, f(x) -> __

Key Concepts

Vertical Asymptotes

Vertical asymptotes occur in rational functions where the function approaches infinity as the input approaches a certain value. In the given graph, vertical asymptotes are present at x = 6 and x = 14, indicating that the function's value becomes unbounded near these x-values. Understanding vertical asymptotes is crucial for analyzing the behavior of rational functions near points of discontinuity.

Horizontal Asymptotes

Horizontal asymptotes describe the behavior of a function as the input approaches infinity or negative infinity. In this graph, the horizontal asymptote is at y = 0, meaning that as x approaches positive or negative infinity, the function's value approaches zero. This concept helps in understanding the long-term behavior of rational functions and their end behavior.

Limits

Limits are fundamental in calculus and algebra, representing the value that a function approaches as the input approaches a certain point. In the context of the question, evaluating the limit of f(x) as x approaches 1 from the left (x -> 1^-) is essential for determining the function's behavior near that point. Understanding limits is key to analyzing continuity and the overall behavior of functions.