How do you write $p (x) = | x - 1 | + 4$ $p(x) = |x-1| +4$ as a piecewise function?

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Answer 1 · 2017-09-07T01:43:21

$p (x) = - x + 5 : x \in (- \infty, 1)$ $p(x)=-x+5 :x in (-oo,1)$
$p (x) = + x + 3 : x \in [1, + \infty)$ $p(x) = +x+3: x in [1, +oo)$

$p (x) = | x - 1 | + 4$ $p(x) =abs(x-1)+4$

$p (x) = - (x - 1) + 4 = - x + 5$ $p(x) =-(x-1)+4 =-x+5$
where $x - 1 < 0 \to x \in (- \infty, + 1)$ $x-1<0 -> x in (-oo, +1)$

$p (x) = + (x - 1) + 4 = + x + 3$ $p(x) =+(x-1)+4 = +x+3$
where $x - 1 \geq 0 \to x \in [1, + \infty)$ $x-1>=0 -> x in [1, +oo)$

This can be more easily visualised from the graph pf $p (x)$ $p(x)$ below.

graph{abs(x-1)+4 [-9.96, 10.04, -0.64, 9.36]}

How do you write p(x) = |x-1| +4p(x)=|x−1|+4p(x) = |x-1| +4 as a piecewise function?