Question

Graph each function. Identify the domain and range.

$g\left(x\right)=\left|x\right|+3$

Short answer

The domain of the function is all real numbers and range is $\left\{y\right|y\ge 3\}$.

The graph of the function is shown below:

Step-by-step solution

Step-1 – Domain and range of the function.

The domain of the function is the set of all input values and range of the function is the set of all output values.

Step-2 – Draw the table.

Find several ordered pairs for the given function

$g\left(x\right)=\left|x\right|+3$

Put various values of x and obtained the respective y values.

The required table is:

Step-3 – Graph the function.

The graph of the function is:

Step-4 – Determine the domain and range.

Here, it can be observed that the domain of the function is the set of all real values because the function can take any value of x.

Also, the range is set of all positive real numbers greater than or equal to 3 or range is $\left\{y\right|y\ge 3\}$.