Question

How to find domain and range

Answer 1

Domain: x ∈ ℝ, 2 ≤ x ≤ 5

Range: y ∈ ℝ, -4 ≤ y ≤ 1

Explanation:

The domain is the possible set of values which can be given as the input (x). The range is the possible set of values which can be given as the output (y).

On a plotted graph, the domain and range can be found by simply reading the possible x and y values. By doing so we can see that x can be between 2 and 5, and y can be between -4 and 1.

x ∈ ℝ and y ∈ ℝ are given in the domain and range to define what set of numbers we are bound to. In the case of this question, it is the real numbers set (denoted by ℝ). More about number sets is outside the scope of this, and your question may not require including the definition, but it is always good practise to define the set when giving the domain and range.

Answer 2

One way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

To find the domain and range, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain. To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y).

Let y = f(x) be a function with an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.

Example:

Find the domain and range of the function y=1x+3−5. To find the excluded value in the domain of the function, equate the denominator to zero and solve for x . So, the domain of the function is set of real numbers except −3 . The range of the function is same as the domain of the inverse function.