How are restrictions and discontinuities created in rational expressions? how can they be accounted for graphically?

I'm not sure what is meant by 'how are zeros created in rational expressions?' I suppose that would just be when the numerator of the rational expression equals zero. Nothing special goes on with the graph in that case; there are simply x-intercepts at those values of x. 
Graphically, this is usually represented by a dashed vertical line indicating a vertical asymptote. 

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