f(x) = x sin(x). I understand that this function is to be regarded as the product of two functions (y = x and y = sin(x)), but what I don't not understand is this bit:

"Using properties of absolute and the fat that |sin x| </= 1, you have

0 </= |x||sin x| </= |x|. Consequently, -|x| </= x sin (x) </= |x|."

What is the meaning of using absolute value to prove that f(x) = x sin (x) resides within the lines y= -x and y = x? What is the justification?

Thank you, I would really like to understand this.