Question

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

Answer 1

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