Use the graph of $f$ in the figure to find the following values or state that they do not exist. <IMAGE>
$f$\left$(1$\right$)$

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Identify the point on the graph where the x-coordinate is 1. This is the point where you will evaluate the function f(x).

Observe the y-coordinate of the point on the graph corresponding to x = 1. This y-coordinate is the value of f(1).

Check if the graph has a defined point at x = 1. If there is a hole or discontinuity at this point, then f(1) does not exist.

If the point is defined and there is no discontinuity, then the y-coordinate at x = 1 is the value of f(1).

Conclude by stating the value of f(1) if it exists, or state that it does not exist if the graph is undefined at x = 1.

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Function Evaluation

Function evaluation involves determining the output of a function for a specific input value. In this case, evaluating f(1) means finding the value of the function f at x = 1. This process requires understanding how to read the graph of the function to identify the corresponding y-value when x is 1.

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Evaluating Composed Functions

Graph Interpretation

Graph interpretation is the ability to analyze and extract information from a visual representation of a function. This includes recognizing key features such as intercepts, peaks, and troughs, as well as understanding the behavior of the function at specific points, which is crucial for answering questions about function values.

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Graphing The Derivative

Existence of Function Values

The existence of function values refers to whether a function is defined at a particular input. For instance, if the graph does not have a point at x = 1, then f(1) does not exist. Understanding this concept is essential for determining if the requested values can be found or if they are undefined.

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