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# graph of f(x)-g(x) watch

1. hey,

how do I sketch the graph of f(x)-g(x)? where f(x)=lx-2l and g(x)=lxl-2

many thanks in advance
2. hey,

how do I sketch the graph of f(x)-g(x)? where f(x)=lx-2l and g(x)=lxl-2

many thanks in advance
So you're essentially being asked to sketch this

First sketch the part where x is > 2. This means the modulus sign will have no effect, as all terms will be positive. In this region you have

Now look what happens for 0 < x < 2. In this region, |x| is unaffected but |x-2| becomes 2 - x (put in some values if this isn't clear to prove it to yourself )

Now the most tricky part: x < 0. The easiest thing is to realise that |x - 2| becomes |x| + 2 in this region, as then we get

and now you're done!
3. For x<0 the terms inside the modulii will be negative so : f(x)-g(x)=-(x-2)+x+2=4
For x>2, the terms indide the modulii will be positive so: f(x)-g(x)=(x-2)-x+2=0

Can you work out what happens in the region 0<=x<=2 ?

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