# A basic function question - with a strange absolute value placement

1. May 21, 2010

### latefreight

1. The problem statement, all variables and given/known data

If f(x) is equal to...

x+9 if x<-3
-2x if |x|$$\leq$$ 3
-6 if x > 3

2. The attempt at a solution

The first and third "segments" of when the function is defined as being x+9 and -6 are pretty straightforward to me, however I am unaware of the significance of the placement of the absolute value of x in the middle if statement of when the function is equal to -2x. Is it significant at all? Does this imply this function is undefined when -3 < x < 0? Or is it, as my initial hunch was, really just some type of a distraction?

2. May 21, 2010

### Staff: Mentor

|x| <= 3 is equivalent to -3 <= x <= 3, so your hunch that this is a distraction is wrong.

3. May 21, 2010

### Dickfore

$$0 \le \left| x \right| \le a \; \Leftrightarrow \; -a \le x \le a$$

4. May 21, 2010

### latefreight

Thank you. I didn't choose my word "distraction" cautiously enough. Since the statements you both posted are equivalent - that was indeed what I needed to know.