How do you write y=3abs(x-1)+2 as a piecewise function?

Oct 8, 2017

y = {$3 x - 1 , x \ge 1$
{$- 3 x + 5 , x < 1$

Explanation:

First, solve for $x - 1 \ge 0$ (an absolute value equation must be a positive number)
So $x \ge 1$

Now, you separate it into 2 different equations:
y = {3(x-1)+2, x >=1
{-3(x-1)+2, x<1 this one has to be the opposite of the first system, so you insert a negative to the first part and change the $\ge$ to $<$
(both the equations are supposed to be in one "{" but I can't type that out properly)

So now you just simplify the equations:
The 1st one becomes:
$3 x - 3 + 2 , x \ge 1$ then
$3 x - 1 , x \ge 1$

The 2nd one becomes:
$- 3 x + 3 + 2 , x < 1$ then
$- 3 x + 5 , x < 1$

So the final answer as a piecewise function is:
y = {$3 x - 1 , x \ge 1$
{$- 3 x + 5 , x < 1$