How do you determine the domain and range of a graph inequalities?

To determine the domain is the same as to determine which numbers appear as the first number (the x-value) in an ordered pair that is part of the graph.
To determine the range is the same as to determine which numbers appear as the second number (the y-value) in an ordered pair that is part of the graph.

Here are some examples:

#y>=x^2+3#

graph{y >= x^2+3 [-11.6, 13.72, 0.15, 12.81]}

Although it is not 100% certain from just the graph, this graph does get wider and wider. Every #x# does appear in some ordered pair on the graph. The domain is all real numbers.

The #y# values that appear start at #3# and go up. We get all numbers greater than or equal to #3#. Inequality: #y >=3#.
If you've learned interval notation, you write: #[3, oo)#

#x^2 + y^2/9 <= 1 #

# graph{x^2 + y^2/9 <= 1 [-5.35, 7.14, -3.105, 3.14]}

Domain (x-values) Go from #-1# to #1# (inequality: #-1<= x <= 1#)(interval: #[-1, 1]#)

Range: #-3# to #3# (inequal: #-3 <= y <= 3#(interval: #[-3, 3]#)

More challenging:

#x^2+y^2 < 9#

graph{x^2+y^2 < 9 [-5.35, 7.14, -3.105, 3.14]}

The dotted line is not included, so we do not include the points at #-3# or at #3#.

Domain: #-3<x<3# (interval #(-3, 3)) Range: #-3<y<3# (interval #(-3, 3))

Last one:

#x- y^2 < 6#

graph{x- y^2 < 6 [-9.87, 30.68, -9.96, 10.32]}

Domain: all real numbers
Range: all real numbers