Question

1. the domain of each piece - wise function is (-∞,∞). graph the function.

f(x) = { 2x if x < 0; -x if x ≥ 0 }

Explanation:

Step1: Graph \(y = 2x\) for \(x<0\)

Pick some \(x\) - values less than \(0\). For \(x=-1\), \(y = 2\times(-1)=-2\); for \(x = - 2\), \(y=2\times(-2)=-4\). This is a straight - line with slope \(m = 2\) and it does not include the point at \(x = 0\). We draw a dashed line at \(x = 0\) for this part of the function.

Step2: Graph \(y=-x\) for \(x\geq0\)

Pick some \(x\) - values greater than or equal to \(0\). For \(x = 0\), \(y=0\); for \(x = 1\), \(y=-1\); for \(x = 2\), \(y=-2\). This is a straight - line with slope \(m=-1\) and it includes the point at \(x = 0\). We draw a solid line at \(x = 0\) for this part of the function.

The graph of \(y = f(x)\) consists of the line \(y = 2x\) for \(x<0\) (dashed at \(x = 0\)) and the line \(y=-x\) for \(x\geq0\) (solid at \(x = 0\)).

Answer:

The graph has a line \(y = 2x\) for \(x<0\) (dashed at \(x = 0\)) and a line \(y=-x\) for \(x\geq0\) (solid at \(x = 0\)).