SOLUTION: Draw the graph of |x-2|-2x. Please explain how you arrived to the anwser. I currently have no concept of absolute values. Thank you

Algebra ->  Algebra  -> Absolute-value -> SOLUTION: Draw the graph of |x-2|-2x. Please explain how you arrived to the anwser. I currently have no concept of absolute values. Thank you      Log On

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Question 159992: Draw the graph of |x-2|-2x.
Please explain how you arrived to the anwser.
I currently have no concept of absolute values.
Thank you
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
Let's look at the absolute value first.
1.abs%28x-2%29=x-2 when x-2%3E=0
2.abs%28x-2%29=-%28x-2%29 when x-2%3C=0
If we expand those two,
1.abs%28x-2%29=x-2 when x%3E=2
2.abs%28x-2%29=-x%2B2%29 when x%3C=2
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.
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Now add that to the other portion of the function(-2x) to get,
1.abs%28x-2%29-2x=x-2-2x when x%3E=2
2.abs%28x-2%29-2x=-x%2B2-2x%29 when x%3C=2
and simplify,
1.abs%28x-2%29-2x=-x-2 when x%3E=2
2.abs%28x-2%29-2x=-3x%2B2%29 when x%3C=2
Two lines with a change point at x=2.
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drawing%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2Cgrid%28+1+%29%2Ccircle%28+2%2C+-4%2C+.3+%29%2Cgreen%28line%28+10%2C-12%2C2%2C-4%29%29%2Cgreen%28line%282%2C-4%2C-10%2C32%29%29%29