Draw the graph $y = | x + 2 | + | x - 3 |$ .

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Solution

$y = | x + 2 | + | x - 3 |$
$case 1 Let x > 3 y = x + 2 + x - 3, y = 2 x - 1, y - 2 x = - 1, \frac{y}{- 1} + \frac{x}{\frac{1}{2}} = 1.$ $case 2 Let x < 3 & x > - 2 y = x + 2 - x + 3, y = 5.$ $case 3 Let x < - 2 y = - x - 2 - x + 3, y = - 2 x + 1, y + 2 x = 1.$

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