Question

Graph each function. Identify the domain and range.

$h\left(x\right)=\{\begin{array}{l}x+3ifx\le -1\\ 2xifx>-1\end{array}$

Short answer

The domain is all real numbers.

The range is all real numbers.

Step-by-step solution

Step-1 – Range and Domain

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 $h\left(x\right)=\{\begin{array}{l}x+3ifx\le -1\\ 2xifx>-1\end{array}$

The graph of the equation $h\left(x\right)=x+3$is linear equation for $x\le -1$.

Here, $-1$satisfies the inequality$x\le -1$. Therefore, end with a closed circle at $x=-1$.

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

Here, $-1$not satisfies the inequality$x>-1$. Therefore, start with an open circle at $x=-1$.

Step-3 – Determine the domain and range.

The domain is all real numbers.

The range is all real numbers.