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

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

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Answer 1 · 2017-10-08T05:05:19

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

Explanation:

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

Now, you separate it into 2 different equations:
$y = {3 (x - 1) + 2, x \geq 1$ $y = {3(x-1)+2, x >=1$
${- 3 (x - 1) + 2, x < 1$ ${-3(x-1)+2, x<1$ this one has to be the opposite of the first system, so you insert a negative to the first part and change the $\geq$ $>=$ 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:
$3 x - 3 + 2, x \geq 1$ $3x-3+2, x>=1$ then
$3 x - 1, x \geq 1$ $3x-1, x>=1$

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

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

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

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