Question

graph each function.
$f(x)=\

$$\begin{cases}x - 2,x\\geq1 \\\\ x + 3,x < 1\\end{cases}$$

$

Explanation:

Step1: Graph \(y = x + 3\) for \(x<1\)

Find two points. When \(x = 0\), \(y=0 + 3=3\). When \(x=1\) (but \(x = 1\) is not included in this part), \(y=1 + 3 = 4\). Draw an open - circle at the point \((1,4)\) and then draw the line \(y=x + 3\) for \(x<1\).

Step2: Graph \(y=x - 2\) for \(x\geq1\)

Find two points. When \(x = 1\), \(y=1-2=-1\). When \(x = 2\), \(y=2 - 2=0\). Draw a closed - circle at the point \((1,-1)\) and then draw the line \(y=x - 2\) for \(x\geq1\).

Answer:

The graph of the piece - wise function \(f(x)=

$$\begin{cases}x - 2,x\geq1\\x + 3,x<1\end{cases}$$

\) is composed of two line segments: one for \(y=x + 3\) (with an open - circle at \((1,4)\)) for \(x<1\) and one for \(y=x - 2\) (with a closed - circle at \((1,-1)\)) for \(x\geq1\).