Draw the graph of the following function: $f (x) = | x - 2 | + | x - 3 |$

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Solution

$f (x) = | x - 2 | + | x - 3 |$
$x < 2$ $f (x) = 2 - x + 3 - x$
$= 5 - 2 x$

$2 \leq x < 3$ $f (x) = x - 2 + 3 - x$
$= 1$

$x \geq 3$ $f (x) = x - 2 + x - 3$
$= 2 x - 5$

$f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 5 - 2 x & x < 2 1 & 2 \leq x < 3 2 x - 5 & x \geq 3 \end{matrix}$

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