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.
