Question Video: Determining the Domain of a Piecewise-Defined Function from Its Graph Mathematics • 9th Grade

Determine the domain of the following function.


Video Transcript

Determine the domain of the following function.

We know that the domain of this function will be the set of all possible 𝑥-values. And on a coordinate grid, that is the 𝑥-axis, the horizontal axis. We see designated values from negative seven all the way to positive seven. However, we should know that the arrows on either side of this graph indicate that this function continues. On the left, we would say that the graph could continue to negative ∞ and on the right to positive ∞.

However, let’s think carefully about what’s happening at zero. When 𝑥 equals zero, does this function have a result? We know that it does because the point is colored in at zero, four. Zero, four is a result, but zero, negative four is not filled in and is therefore not a result of this function. Since we do have a result at zero, we can confirm that there’s a domain of all real numbers.

This question hasn’t asked us for a range. But if we wanted to add the range, that would be the output values, the set of possible 𝑦-values. And we see that there are two possible values: one value at four and one value at negative four. In set notation, we could write that the range is therefore negative four and four. As the question has only asked us to identify the domain, we can simply say that the domain is all reals.

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