Question

Graph each function. Identify the domain and range.

$g\left(x\right)=\{\begin{array}{l}-1ifx<0\\ -x+2ifx\ge 0\end{array}$

Short answer

The domain is all real numbers.

The range is $\left\{y\left|y\le 2\right|\right\}$

Step-by-step solution

Step-1 – Range and Domain 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 graph.

The given function is

$g\left(x\right)=\{\begin{array}{l}-1ifx<0\\ -x+2ifx\ge 0\end{array}$

The graph of the equation $g\left(x\right)=-1$is constant function for $x<0$.

Here, $-1$does not satisfies the inequality $x<0$. Therefore, stop with open circle at $x=-1$.

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

The required table is:

The graph of the equation $g\left(x\right)=-x+2$is linear function for $x\ge 0$.

Here, 0 does satisfies the inequality$x\ge 0$. Therefore, start with closed circle at $x=0$.

The graph of the function is shown below:

Step-3 – 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.

The range is $\left\{y\left|y\le 2\right|\right\}$