On which interval is the graph of \(y=|x|+|x-4|\) horizontal?

Correct answer: \(0\le x\le 4\)

For \(0\le x\le 4\), we have \(|x|=x\) and \(|x-4|=4-x\). Hence \(y=x+(4-x)=4\), a constant value, so the graph is horizontal throughout this interval. For \(x<0\) and \(x>4\), the slopes are \(-2\) and \(2\), respectively, so the graph is not horizontal there. Exam tip: For a function involving absolute values, first identify the points where the expressions inside the modulus signs become zero.