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Sketch the graph of a given function

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Based on the information, create a sketch of the function on the axes provided. Please provide detailed explanation. ** Please see the attached file for the complete problem description **

-Increasing and constant: none
-Decreasing: (-infinity, 2)... (please see the attached file)


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We pick up those conditions, from the above, which give us a primary idea about the function
Given that Domain, (condition 5) is the set of all real numbers except 2; hence there should be an (x-2)n in the denominator of f(x), where n is some natural number.
This is supported by the given condition (condition 6) that there is a vertical asymptote at x=2
From the condition 8, we can see that f(x) should have a factor 2x-3 in its numerator.
From the condition 7, the behavior of the function, while x moves towards ∞ or ...

Solution Summary

This solution provides a step-by-step explanation for how to sketch the graph of a given function under a set of conditions/observations known about it.