10. While the domain of a rational function depends on DIVAH, what do you think the range of a rational function depends on? Give an example.
The range of a rational function would depend on the y-values. For example, since the domain is the restrictions or "bad values" we can always see those as x-values, or the vertical asymptotes. However if we were to find the range, we would include restrictions on the horizontal asymptote. But, we have to remember, the graph can sometimes cross the horizontal asymptotes, unlike the vertical asymptotes. This would be difficult to find because at times when it crosses then there are no restrictions, there wouldn't be a range.
The domain restrictions on this graph would be 2 and -2. We can clearly see the vertical asymptotes are never crossed. However, the range restriction of 9 is crossed by the middle graph and technically now has no restrictions since it was crossed.
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