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Wikkibahi · Dec 5, 2011, 06:07 AM

I attach the following Math Pdf File, Please Open it and solve my Problem as soon as possible.
Thanks a lot for this.

ebaines · Dec 5, 2011, 06:22 AM

Theyt want you to graph $f(x) = x - |x|$ for $x$ in the domain [-3,3].

Start by calculating the value for f(x) for each of several key values of x. For example, at one end of the domain you have x = -3, so determine f(-3):
$<br /> f(-3) = -3\ -\ |-3| = -6.<br />$

(Note that the absolute value of -3 is 3.) Now continue for other key points - I suggest trying x = -1, x=0, x = 1, x=2 and x=3. You should find that the graph is basically a bent line. Post back with what you get and we'll check it for you.

Aurora2000 · Dec 5, 2011, 09:00 AM

If they want $f(x):=x-|x|$ , see ebaines's comment.

If they want $f(x):=x-[x]$ (which produces a graph more like "saw tooth"), you should use the definition of $[x]$ : $[x]:=\max_{d\in \mathbb{Z}, d\leq x} d$ . It is also called "integer part" function (this because you simply remove the decimal part for positive numbers - for negative numbers it is a little bit different, for negative integers [] acts like identity, while for negative non integers you remove the decimal part and subtract 1): e.g. [3.554]=3, [1.473]=1, [0,833]=0, [e]=2, etc. but [-3.2]=-4, [-1]=-1, [-e]=-3 etc.

So $f(\mathbb{Z})=\{0\}$ , find the rest.