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    Hi,
    Basically, I've found that when you have to do:

    f(|x|)

    you need to reflect whatevers on the right hand side in the y axis.

    However I don't understand why?
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    All of the x values that were negative now become positive by the modulus
    for example f(-1) = f(1) so it is a reflection in the y axis
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    When you apply the modulus function to the independent variable (x values), all the values of the input that are negative are transformed into positive values in the function. This has the effect that all negative inputs have the same outputs as the corresponding positive inputs, so the part of the graph on the left of the y axis is equivalent to the part of the graph on the right of the y axis reflected in the y axis. For example, if you take f=|x|³, an input of -3 and 3 both have an output of 27, and -5.5 and 5.5 both have an output of 166.375, so the function becomes an even function.
 
 
 
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