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Sketch the graphs of the functions that have the given limits and values (there are multiple answers)

Sketch the graphs of the functions that have the given limits and values (there are-example-1

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Answer:

see attached

Explanation:

The required graph will have a "hole" at (3, 2). That is, the function will be undefined there.

Functions with a hole

A rational function will be undefined at x=3, but defined nearby, if its numerator and denominator have cancelling zeros at x=3. For the purpose here, "nearby" values must approach 2 as x approaches 3 from either direction.

Graphs of a couple of such functions, f(x) and g(x), are shown in the attachment. There are an infinite number of possibilities.

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Additional comment

A "hole" is identified on a function's graph by an open circle, indicating the function is not defined there.

Sketch the graphs of the functions that have the given limits and values (there are-example-1
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