Question

graph the function.
f(x)=\begin{cases} |x| &\text{for }x < 4\\ -x + 8&\text{for }xgeq4 end{cases}

Explanation:

Step1: Analyze \(y = |x|\) for \(x<4\)

When \(x < 0\), \(y=-x\); when \(0\leq x < 4\), \(y = x\). Plot points for this part. For example, when \(x=- 3,y = 3\); when \(x = 0,y = 0\); when \(x=3,y = 3\).

Step2: Analyze \(y=-x + 8\) for \(x\geq4\)

Find the \(y\) - intercept of \(y=-x + 8\) (when \(x = 4,y=-4 + 8=4\); when \(x=8,y=-8 + 8 = 0\)). Plot points \((4,4)\) and \((8,0)\) and draw the line for \(x\geq4\).

Answer:

The graph consists of the V - shaped graph of \(y = |x|\) for \(x<4\) and the line \(y=-x + 8\) for \(x\geq4\) with a closed - circle at the point \((4,4)\) (since the function is defined as \(y=-x + 8\) when \(x = 4\)).