10. While the domain of a rational function on DIVAH, what do you think the range of a rational function depends on? Give an example.
Domains depends on DIVAH meaning domain is vertical asymptotes and holes. The domain of a rational function is all x-values that the graph can touch written in limit notation. It is either represented by a vertical asymptote or a hole to show the restrictions of the graph. For example if we had x^3/x-2 our domain would be x=2; therefore, domain is all x values except x=2. Opposite of this would be the range, all y-values, and I think this will depend on the graph. We see where the graph starts looking at the y-value and see the direction it is going.
For example, if we take a look at this graph see that it covers all y-values without any limits or holes. For this reason since there is no restrictions in the y-values meaning the range is all y-values which is written (-∞, ∞ ).
In the graph to the right, we see that the graph is heading up and down at all y-values. However, looking closer at the graph we see that it does not touch the graph at y=0. This represents a limit in the graph so just like the x-intercepts this would be our bad values. It would be written similarly to the domain only it will be representing the range. In this case it would be (-∞ ,0) u (0,∞ ).
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