Use the graph of the rational function in the figure shown to complete each statement in Exercises 9–14.
As x -> -3^-, f(x) -> __

Key Concepts

Rational Functions

A rational function is a function that can be expressed as the ratio of two polynomials. The general form is f(x) = P(x)/Q(x), where P and Q are polynomials. Understanding rational functions is crucial for analyzing their behavior, including identifying asymptotes and intercepts, which are key to interpreting their graphs.

Asymptotes

Asymptotes are lines that a graph approaches but never touches. Vertical asymptotes occur where the function is undefined, typically where the denominator equals zero, while horizontal asymptotes indicate the behavior of the function as x approaches infinity. In this case, the graph has vertical asymptotes at x=6 and x=14, and a horizontal asymptote at y=0.

Limits

Limits describe the behavior of a function as the input approaches a certain value. In this context, evaluating the limit of f(x) as x approaches -3 from the left (denoted as x -> -3^-) helps determine the corresponding output value. Understanding limits is essential for analyzing the continuity and behavior of rational functions near their asymptotes.