Graphing f|x| from f(x)

The input of f(x) is x
Whereas the input of f(|x|) is |x|
 x=|x| when x is positive.
Example
f(x) = sinx


f(|x|) = sin(|x|)
Therefore graph of f(x) is same as that of f(|x|) for positive values of x only i.e on the right side of X-Axis


x =-|x| for negative values of x.
That implies if we input negative numbers in f(|x|),
we end up giving -x as input and since x is negative in this case, -x is a positive number with the same value.
Example when x=2
f(2) = f(|2|) 
But if x=-2
f(|-2|) =f(2)
Hence f(2)= f(|2|) = f(|-2|)
When x=-3
f(|-3|) = f(3) 
For x=-4
f(|-4|)=f(4)


Whatever number, we may use, it turns positive before entering f(|x|) and hence is determined by f(x) where x is positive number
Therefore f(|x|) is determined by f(x) with only positive inputs.
For f(|x|)
f(x)= f(-x)
Hence whatever shape is f(|x|) is on right side of X-Axis as sketched previously, is on left side as well.


f(|x|) is an even function.



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