I am having trouble making a piece wise function i will draw it out

Question

venomblast · Answer

$$\frac{ 1 }{ 2 }e ^{-|x|} , -\infty<x<\infty $$

mww · Answer

This one isn't too hard if you know the definition of absolute value.

$$|x| = x,   \forall x > 0$$
$$|x| = -x, \forall x \le 0$$

Thus $$\frac{ 1 }{ 2 } e^{-|x|} = \frac{ 1 }{ 2 } e^{-x} ;  \forall x > 0$$
$$\frac{ 1 }{ 2 } e^{-|x|} = \frac{ 1 }{ 2 } e^{x} ;  \forall x \le 0$$

Alternative approach.
The graph of f(|x|) is simply the graph of f(x) where x > 0 reflected about the y -axis. (i.e. draw the graph of y = f(x) and then make the left side of the graph mirror the right side (the left side doesn't matter). This property exists because f(|x|) is an even function.

So you can draw the right side of 
$$y = \frac{ 1 }{ 2 }e^{-x}$$, then reflect this about the y-axis.

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