Question

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

Answer 1

y = {`3x-1, x>=1`
{`-3x+5, x<1`

Explanation:

First, solve for `x - 1 >= 0` (an absolute value equation must be a positive number)
So `x >= 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 `>=` 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:
`3x-3+2, x>=1` then
`3x-1, x>=1`

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

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