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

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

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Answer 1 · 2018-01-16T05:40:13

$color(blue)(|x+1| - 4 = { x+1, if x>= (-1)})$

$color(blue)(|x+1| - 4 = { -x-1, if x< (-1)})$

Explanation:

Given:

$color(red)(y=f(x)=|x+1|-4)$

We draw the graph of this function first

enter image source here

$color(green)(Step.1)$

We find the boundary line first.

Later, once we find the "Piece-wise Functions", we can graph those as well and compare the graphs.

We can accomplish this process by setting what is inside absolute value to ZERO, and then solving for $color(red)x$ .

So, when

$x+1 =0$

we get

$color(blue)(x = (-1))$

$color(green)(Step.2)$

When $(x+1)$ is Positive, we just consider the expression as it is,

but if $(x+1)$ is Negative, we must negate the whole expression

$color(green)(Step.3)$

Hence,

our required Piece-wise Functions are

$color(blue)(|x+1| - 4 = { x+1, if x>= (-1)})$

$color(blue)(|x+1| - 4 = { -x-1, if x< (-1)})$

We will graph the Piece-wise Functions below:

enter image source here

Hope this helps.

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

1 Answer

Explanation:

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