Question

Graph each function. Identify the domain and range.

$h\left(x\right)=\{\begin{array}{l}-1ifx<-2\\ 1ifx>2\end{array}$

Short answer

The domain of the function is $\left\{x\right|x<-2 or x>2\}$ and range is $\{-1,1\}$.

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 graph.

The given function is$h\left(x\right)=\{\begin{array}{l}-1forx<-2\\ 1forx>2\end{array}$

The graph of the equation $h\left(x\right)=-1$is constant function for$x<-2$.

Here, $-2$does not satisfies the inequality $x<-2$. Therefore, stop with open circle at $x=-2$.

The graph of the equation $h\left(x\right)=1$is constant function for $x>2$.

Here, 2 does not satisfies the inequality $x>2$. Therefore, starts with open circle at $x=2$.

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 $\left\{x\right|x<-2 or x>2\}$.

Since, the value of the function can be either 1 or $-1$. Thus, the range is $\{-1,1\}$.