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

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Answer 1 · 2017-04-16T21:29:50

Use the definition of the absolute value function:

$|a| = {(a; a >=0),(-a;a<0):}$

Given: $p(x) = |x-1| +4$

Please observe that $a = x-1$ with regard to the definition:

$|x-1| = {(x-1; x-1 >=0),(1-x;x-1<0):}$

Simplify the inequalities

$|x-1| = {(x-1; x >=1),(1-x;x<1):}$

Add 4 to both sides:

$|x-1|+4 = {(x-1+4; x >=1),(1-x+4;x<1):}$

Simplify the right side and substitute $p(x)$ on the left:

$p(x) = {(x+3; x >=1),(5-x;x<1):}$

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