Question Video: Determining the Domain and the Range of a Rational Function given Its Graph Mathematics

Determine the domain and the range of the function represented in the shown figure.


Video Transcript

Determine the domain and range of the function represented in the shown figure.

The domain represents the 𝑥-values and the range represents the 𝑦-values. Let’s first look at the domain. Almost all of the 𝑥-values have a place to land somewhere on the graph, except for one of them. Values that are really close to negative three have places to land. And in between every single integer — the fractions; those have places to land as well. But it’s every single number, except for negative three.

So the domain will be the real numbers, except for negative three, so the reals minus negative three. Here we can see that almost all of the 𝑦-values have somewhere to go, except for the value of negative four. So the range would be all real numbers, except for negative four. So it’d be all reals minus negative four. So again a domain is the reals minus negative three and the range would be the real numbers minus negative four.

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