Use the graph of f in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>
${\lim }_{x\to 1^{-}}f\left(x\right)$

Key Concepts

Limits

A limit describes the value that a function approaches as the input approaches a certain point. In this context, we are interested in the left-hand limit, denoted as lim_{x→1^{-}}f(x), which examines the behavior of the function f(x) as x approaches 1 from values less than 1. Understanding limits is crucial for analyzing continuity and the behavior of functions at specific points.

Left-Hand Limit

The left-hand limit refers specifically to the value that a function approaches as the input approaches a certain point from the left side. It is denoted as lim_{x→c^{-}}f(x) for a point c. This concept is essential when determining the overall limit of a function at a point where the function may behave differently from the left and right sides.

Existence of Limits

For a limit to exist at a point, both the left-hand and right-hand limits must approach the same value. If they do not match, or if one or both limits do not exist, we conclude that the limit at that point does not exist. This concept is vital for understanding discontinuities in functions and for providing explanations when limits are found to be non-existent.