Use the graph of f in the figure to find the following...

Use the graph of $f$ in the figure to find the following values or state that they do not exist.
a. $f(2)$ $\begin{array}{lll}\text { b. } \lim _{x \rightarrow 2} f(x) & \text { c. } \lim _{x \rightarrow 4} f(x) & \text { d. } \lim _{x \rightarrow 5} f(x)\end{array}$

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Key Concepts

One-Sided Limits

One-sided limits involve looking at the behavior of a function as x approaches a point from only one direction, either from the left or the right. They are especially useful in cases where the behavior of the function is different on each side of the point, which can indicate a discontinuity or a jump in the graph.

Continuity

Continuity at a point means that the function's limit as x approaches that point is equal to the function value at that point. This concept is pivotal when using a graph to determine if a function behaves smoothly at a point or if there are any jumps or removable discontinuities.

Function Value

This concept refers to the output of the function at a specific input. It is the actual value assigned by the function when you substitute the given input into the function, and it is derived directly from the graph by locating the y-coordinate corresponding to the x-value.

Limit of a Function

The limit of a function as x approaches a certain value describes the behavior of the function near that point, regardless of the actual function value at that point. It is determined by observing the behavior of the function's outputs as x gets arbitrarily close to the specified value.

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