Question

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

Answer 1

Hint: Here we will find the domain and the range of graph inequalities, it is the same as to determine which numbers will appear as the first number that is the variable “x” in the ordered pair that is the part of the graph and to determine the range is just same as to determine which number appear as the second number that is the “y” value which will be the ordered pair in the part of the graph.

Complete step by step solution:
Domain can be expressed as the set of all the “x” values, the independent quantity for which the function $ f(x) $ exists whereas, the range is the set of all the “y” values and it is dependent quantity which will result from substituting all the values that is the domain into the function.
Let us take an example:
 $ y \geqslant {x^2} + 3 $
Place, $ x = 1,2,3,4,.... $ one by one in the above equation.
First place, $ x = 1 $
 $ y \geqslant {1^2} + 3 $
Simplify the above equation,
 $ y \geqslant 4 $
So, $ (x,y) = (1,4) $
Similarly, $ x = 2 $
 $ y \geqslant {2^2} + 3 $
Simplify the above equation,
 $ y \geqslant 4 + 3 $
So, \[(x,y) = (2,7)\]
Hence for the every “x” value it comes with the ordered pair on the graph and the graph becomes wider and wider and also, the domain and the range are all the real numbers.

Note: Do not get confused with the domain and the range with the solution to an inequality, these two have different concepts. Domain and range mean all the possible values for “x” and “y” to be substituted in the inequality.