Domain is the complete set of all possible real values of the function. Range is the complete set of all possible output values of the function.Consider a function
Domains and Range

Here Domain is the possible values of independent values of x and Range is all possible dependent values of y.

Domain and Range Calculator is used to calculate the domain and range of given function and plot a graph for the given set of domain and ranges. Provided is the block where you are supposed to enter your function to get the answer. 
Let us analyze the method to find the domain and range.

Step 1 : Read the given problem and note the given function. Choose desired values of x (domain) and find the values of the function y.

Step 2 : Write the domain and range of the function using the interval notation and Plot a graph.

Below are given some solved problems on Domain and range which may be helpful for you.

Solved Examples

Question 1: Find the domain and range of function f(x) = x + 2
Solution:
 
Step 1 : The given function is y = x + 2.
             Let us take domain values as {-1.6, -1.8, -2, -2.2}

                    For x = -1.6, y = -1.6 + 2 = 0.4
                          x = -1.8, y = -1.8 + 2 = 0.2
                          x = -2, y = -2 + 2 = 0
                          x = -2.2, y = -2.2 + 2 = -0.2

              The range values are {0.4, 0.2, 0, -0.2}
              Hence the set of real numbers are domain values of given function and the range will vary based on the function f(x).

Step 2 :   Domain  {x $\epsilon$ R} for all real numbers R
               Range { y $\epsilon$ R}

              The graph can be plotted by taking domain values on x-axis and range values on y-axis.
 Domains and Range
 

Question 2: Find domain and range of $\frac{1}{2x - 1}$.
Solution:
 
Step 1: The given function is y = $\frac{1}{2x - 1}$.
       
            Let us take domain values form -0.5 to 1.5 as {-0.5, 0, 0.5, 1.5}
   
                          For x = -0.5, y = $\frac{1}{2(-0.5) - 1}$ = -0.5
                       
                                x = 0,  y = $\frac{1}{2(0) - 1}$ = -1
 
                               x = 0.5,  y = $\frac{1}{2(0.5) - 1}$ = $\infty$ = not defined

                               x = 1, y = $\frac{1}{2(1) - 1}$ = 1

                               x = 1.5, y = $\frac{1}{2(1.5) - 1}$ = 2

The range values are {-0.5, -1, 1, 2} for the domain {-0.5, 0, 1, 1.5}. Hence the set of real numbers are domain values of given function and the range will vary based on the function f(x).

Step 2: Domain {x $\epsilon$ R : x $\neq$ $\frac{1}{2}$}

            Range {y $\epsilon$ R : y $\neq$ 0}

The graph can be plotted by taking domain values on x-axis and range values on y-axis.
Domains and Range