How do you graph $y = | x - 4 | - 6$ $y=abs(x-4)-6$ ?

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How do you graph $y = | x - 4 | - 6$ $y=abs(x-4)-6$ ?

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Answer 1 · 2018-06-27T12:41:56

See below

Explanation:

Firstly, find the two different absolute value cases, so:

$| x - 4 | = x - 4 ($ $|x-4|=x-4 ($ when $x - 4 \geq 0 \to x \geq 4)$ $x-4>=0 -> x>=4)$ and $- 1 (x - 4) ($ $-1(x-4)($ when $x < 4)$ $x<4)$
$| x - 4 | = x - 4 ($ $|x-4|=x-4 ($ when $x \geq 4)$ $x>=4)$ and $4 - x ($ $4-x($ when $x < 4)$ $x<4)$

Sub the two different cases back into the original $y = | x - 4 | - 6$ $y=|x-4|-6$ equation

When $x \geq 4$ $x>=4$ ,
$y = (x - 4) - 6$ $y=(x-4)-6$
$y = x - 10$ $y=x-10$

When $x < 4$ $x<4$ ,
$y = (4 - x) - 6$ $y=(4-x)-6$
$y = - x - 2$ $y=-x-2$

Now, simply graph the line $y = x - 10$ $y=x-10$ for the region $x \geq 4$ $x>=4$ and graph $y = - x - 2$ $y=-x-2$ for the region $x < 4$ $x<4$

graph{y=|x-4|-6 [-4.96, 15.04, -7.76, 2.24]}

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How do you graph $y = | x - 4 | - 6$ $y=abs(x-4)-6$ ?

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How do you graph $y = | x - 4 | - 6$ $y=abs(x-4)-6$ ?