this is just the kind of question that does not get much help here. Any web search will provide lots of discourses on the topic. No doubt your text does, as well.
So, a long essay here will probably not shed any more light on your confusion.
Do you have a particular question that is giving you trouble? If so, give us a little something to go on here.
To just play around with rational functions, visit wolframalpha.com and enter the function, and it will show you the graph. Tweak the parameters, and see what happens. It may help you to interpret the graphs in your text.
Explain how to find the equation of the vertical asymptotes of a reciprocal function in full details.
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