Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>
lim x→−1 f(x)

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Identify the point of interest on the graph, which is x = -1.

Observe the behavior of the function f(x) as x approaches -1 from both the left and the right.

Check if the values of f(x) from the left (x approaches -1 from the negative side) and from the right (x approaches -1 from the positive side) are approaching the same value.

If the left-hand limit and the right-hand limit are equal, then the limit exists and is equal to that common value.

If the left-hand limit and the right-hand limit are not equal, then the limit does not exist.

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Limits

A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. It helps in understanding how functions behave near points of interest, including points of discontinuity or where the function is not explicitly defined. Evaluating limits is crucial for determining the continuity of functions and for finding derivatives.

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Graphical Analysis

Graphical analysis involves interpreting the visual representation of a function to understand its properties, such as continuity, limits, and asymptotic behavior. By examining the graph, one can identify trends and behaviors of the function as it approaches specific x-values, which is essential for evaluating limits and understanding the function's overall behavior.

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Continuity

Continuity refers to a property of a function where it is uninterrupted and has no breaks, jumps, or holes in its graph. A function is continuous at a point if the limit as x approaches that point equals the function's value at that point. Understanding continuity is vital for evaluating limits, as discontinuities can affect the limit's existence and value.

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