Phillip R. answered • 09/06/14
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this is not a transformation. It is completely new function.
Think about the two terms lxl and x
When x is a positive number or zero, these two terms have the same value.
Therefore lxl - x = 0
So for x ≥ 0, the f(x) = 0
When x is a negative number, lxl will be positive but x will be negative and we get l2xl
So from x = 0 and going to the right, the graph lies on the x-axis which is where y = o
For values to the left of x = 0, the graph is a straight line with a slope = -2
Phillip R.
When we subtract a negative number, of course we get a positive. So -x has a value of absolute value of x, making it positive. If we just said -(-x) = x then the expression would have a negative value because we are now considering only negative values for x. And so we add the absolute value notation. Literally, the value is 2x but again if we are considering only negative values of x, 2x woold be negative which it's not. Remember, absolute value of x = -x whenever x is a negative number. It sounds wrong to say absolute value is negative but try it with an actual number, for example -3 and you'll see what I mean.
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09/06/14
Forrest C.
09/06/14