A LEVEL MATHEMATICS

The Mailbox

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.

Thereafter,

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