What is the domain and range of #y=x^2#?

1 Answer
Mar 26, 2015

This is an equation (and a function) whose graph we should know:

graph{x^2 [-20.19, 20.36, -2.03, 18.25]}

The domain is the set of all allowed #x# values. Although it is not 100% certain from the graph, it is clear from the equation, that for any number you put in for #x# you will get one and only one value for #y#. The domain is all real numbers . (The interval #(-oo, oo)#)

The range is the set of all #y# value the graph actually includes. Looking at the graph (and thinking about #x^2#, it becomes clear that #y# will never have a negative value.
It is not 100% certain from the graph, but every number that is NOT negative will be used as a #y# value. The range is #[0, oo)#