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Modulus function graph question

Posted by White Group Mathematics on October 1, 2014 at 10:05 AM

Hello, I've never encountered this sort of question before and I don't know how to approach it. Could you explain it please?


The functions f and g are defined on the domain of all real numbers by f(x)= |x-2| and g(x)= |x|-2.


Sketch the graph of f(x) - g(x).

Student X

First, let us define each of the individual modulus functions:


|x-2| = x-2 if x≥2

        = 2-x if x<2


|x|= x if x≥0

    = -x if x<0


There are 3 critical regions, namely x<0, 0 ≤ x < 2 and x≥2


For the extreme left critical region, ie x<0,


f(x) - g(x) = |x-2| - |x| + 2 = (2-x) - (-x) +2 = 4


In other words, you shall draw a horizontal line y=4 all the way from x=-∞ to x=0.




for the next critical region 0 ≤ x < 2,


f(x) - g(x) = |x-2| - |x| + 2 = (2-x) - (x) +2 = 4-2x


In this case, you shall draw the line with equation y=4-2x from x=0 to x=2.


I shall let you figure out the final graph you need to draw for the remaining critical region, which shouldn't be all too difficult if you can understand what I have explained thus far.


Hope it helps. Peace.

Best Regards,

Mr Koh

Categories: Math Queries

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