How do you find the domain and range of #y = x^2 - 3#?

1 Answer

Answer:

#x in RR, y>=-3#

Explanation:

The domain is the list of valid #x# values. Here, there are no values of #x# that are disallowed (0 is ok, small positive and negative values are ok, big positive and negative values are ok). And so we can say that the domain is:

#x in RR#

The range is the list of resulting values after we plug in #x# values. See that the smallest value #x^2# can be is 0 - it can't be negative. And so the smallest value #x^2-3# can be is #-3#. This means the range is:

#y>=-3#

Here's the graph that will show this:

graph{x^2-3}