Suppose I have any modular function, for example:

$$f(x) = |2x + 4| + 3$$

I can rewrite the function in the following way:

$$f(x) = \left\{\begin{matrix} 2x + 7, \;\; x \geq -2\\ -2x -1, \;\; x < -2 \end{matrix}\right.$$

right?

Okay, the question is: how do I know that the first condition is $$\geq$$ and second condition is < and not vice-versa?

Thank you,
Rafael Andreatta

It doesn't matter, because |x| is a continuous function. What's the value of f(x) for x=-2?

It doesn't matter, because |x| is a continuous function. What's the value of f(x) for x=-2?
1. You mean, because |x| is a continuous function or because f is a continuous function?

2. What if it was not continuous?

Office_Shredder
Staff Emeritus