Question

piecewise functions:
graph each function.
$f(x)=\

$$\begin{cases}x + 1,x\\geq0 \\\\ 2x - 3,x < 0\\end{cases}$$

$

Explanation:

Step1: Graph \( y = x + 1\) for \(x\geq0\)

Find two points. When \(x = 0\), \(y=0 + 1=1\). When \(x = 2\), \(y=2 + 1=3\). Plot \((0,1)\) (closed - circle since \(x = 0\) is included) and \((2,3)\), then draw a line through them for \(x\geq0\).

Step2: Graph \(y = 2x-3\) for \(x<0\)

Find two points. When \(x=-1\), \(y=2\times(-1)-3=-5\). When \(x = - 2\), \(y=2\times(-2)-3=-7\). Plot \((-1,-5)\) and \((-2,-7)\) (open - circle at \(x = 0\) for this part since \(x = 0\) is not included in \(x<0\)), then draw a line through them for \(x<0\).

Answer:

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

$$\begin{cases}x + 1,x\geq0\\2x-3,x<0\end{cases}$$

\) is composed of two line segments: one for \(y=x + 1\) (with a closed - circle at \((0,1)\)) for \(x\geq0\) and one for \(y = 2x-3\) (with an open - circle at the \(y\) - value when \(x = 0\) for this part) for \(x<0\).