Review question

# Can we sketch the graph of $y = |x| + |x-1| + |x-4|$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9130

## Question

If $p$ is real the value of $\big|p\big|$ is $p$ if $p \ge 0$ and is $-p$ if $p < 0$.

By considering the ranges $x < 0$, $0 \le x < 1$, $1 \le x < 4$ and $x \ge 4$, show that the graph of $\begin{equation*} y = \big|x\big| + \big|x-1\big| + \big|x-4\big| \end{equation*}$

consists of four line segments and give the equation of each segment. Sketch the graph.

Calculate the roots of the equations

1. $\big|x\big| + \big|x-1\big| + \big|x-4\big| = 6 - \dfrac{1}{3}x$,
2. $\big|x\big| + \big|x-1\big| + \big|x-4\big| = \dfrac{1}{x}$.