Question

graph the function.
f(x) = { 2x, for x < 0; x + 6, for x ≥ 0 }
choose the correct graph below.

Explanation:

Step1: Analyze \(f(x)=2x\) for \(x < 0\)

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y = 2x\) (\(x<0\)), the slope \(m = 2\) and the y - intercept is \(0\). We use an open - circle at \(x = 0\) since \(x<0\). When \(x=- 5\), \(y=2\times(-5)=-10\).

Step2: Analyze \(f(x)=x + 6\) for \(x\geq0\)

For the line \(y=x + 6\) (\(x\geq0\)), the slope \(m = 1\) and the y - intercept is \(6\). We use a closed - circle at \(x = 0\) since \(x\geq0\). When \(x = 0\), \(y=0 + 6=6\); when \(x=5\), \(y=5 + 6=11\).

Answer:

Without seeing the actual graphs A, B, C, D, we can describe the correct graph: It should have a line \(y = 2x\) with an open - circle at the origin (for \(x<0\)) and a line \(y=x + 6\) with a closed - circle at the point \((0,6)\) (for \(x\geq0\)). If you provide the details of the graphs A, B, C, D, we can further determine the correct option.