Sketch the function $y = | x - 2 |$ in the interval $(- 1, 3)$ . Is this function continuous.

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Solution

$y = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} - (x - 2), & x < 2 0, & x = 2 x - 2, & x > 2 \end{matrix}$
It consists of two straight lines and a point(2,0).
. Continuous but not differentiable at $x = 2.$
Ans: 3

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