Question

In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation.

Short answer

The domain is$\left(-\infty ,\infty \right)$and the range is$[2,\infty )$.

Step-by-step solution

Step 1.  Given information

Consider the below graph of a function.

The main objective is to determine the domain and range of the function in interval notation.

Step 2. Definitions.

• The domain of a function is defined as the set of all $x$-values that the function takes as input values.
• The range of a function is defined as the set of all $y$values that the function takes as output values.

Step 3. Explanation

From the given graph, the input values of the function are all the $x$values.

So, it is clear that the domain of the function is all $x-$values, that is$\left(-\infty ,\infty \right)$.

From the graph, it is clear that the output values that the function results are role="math" localid="1646873097781" $y\ge 2$.

So, the range is$[2,\infty )$.