Use the graph of the rational function in the figure shown to complete each statement in Exercises 9–14.

As x -> -3^-, f(x) -> __

Verified step by step guidance

1. Identify the point of interest on the x-axis, which is x approaching -3 from the left (x → -3⁻).
2. Observe the behavior of the function f(x) as x approaches -3 from the left side on the graph.
3. Note whether the function values are increasing or decreasing and whether they approach a finite number or infinity.
4. From the graph, as x approaches -3 from the left, the function values approach 0 from below, indicating f(x) approaches 0⁻.
5. Conclude that as $x\; o\; -3^\{-\}$, $f(x)\; o\; 0^\{-\}$.

Key Concepts

Vertical Asymptotes

Vertical asymptotes occur where the function approaches infinity or negative infinity as x approaches a specific value. They represent values of x that make the denominator zero in a rational function, causing the function to be undefined. In the graph, vertical asymptotes are shown at x = 6 and x = 14.

Horizontal Asymptotes

A horizontal asymptote describes the behavior of a function as x approaches positive or negative infinity. It indicates the value that the function approaches but does not necessarily reach. In this graph, the horizontal asymptote is y = 0, meaning the function values get closer to zero as x becomes very large or very small.

Limits and One-Sided Limits

Limits describe the value a function approaches as the input approaches a certain point. One-sided limits consider the approach from only one side (left or right). The question asks for the limit of f(x) as x approaches -3 from the left, which involves analyzing the graph's behavior near x = -3 from values less than -3.