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. $f(1)$
b. $\lim _{x \rightarrow 1} f(x)$
c. $f(0)$
d. $\lim _{x \rightarrow 0} f(x)$
(FIGURE CAN'T COPY)

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Key Concepts

Function Evaluation

Function evaluation is the process of finding the output value of a function for a given input by substituting that input into the function. When using a graph, this involves locating the point corresponding to the input value on the x-axis and reading the associated y-value, which represents the function’s value at that point.

Limits

The concept of limits describes the behavior of a function as the input approaches a specific value, even if the function is not defined at that point. Graphically, the limit is determined by observing the y-values that the function approaches as the x-values get arbitrarily close to the target point, which may differ from the actual function value at that point.

Continuity and Discontinuity

Continuity occurs when a function’s limit at a point is equal to its actual value at that point, resulting in an unbroken curve in the graph. Discontinuity, such as a jump discontinuity, happens when there is a break in the function’s graph, meaning the limit as x approaches a point might exist and differ from the function's defined value, or the limit might not exist at all.

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