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

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.

## Domain and Range Problems

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.

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.

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