When solving a piece-wise function. Can I plug in any value I want for x?

Question

I am currently studying piece-wise functions for a final and I was wondering if I could plug in any value for x for example:
f(x)+{2x-2, if x<-3} and I mean x as in the x next to the 2. I understand I have to follow the rule x<-3 but I was wondering if I could plus in any value that's less than -3

Answer 1

I think you mean

 

f(x) = { 2x - 2 , if  x < -3 }

 

 

You can plug in any value of x, as long as it is less than -3.

Answer 2

Yes.  That is the point of a piecewise function.

For f(x) = {2x-2, if x<-3}

Then you plug in any value for x that is under -3

and solve for f(x).

 

In order to solve for any vaule of x ≥-3 you would

have to have another "piece" of the function

defining how to find x within that range.

Answer 3

Yes, that is simply saying the domain of the function is the interval (-∞, -3) so you can plug in any value less than -3 into that part of the function. If your piece-wise function had multiple "pieces," you would simply use whichever one is relevant for a given x, and the pieces would not be allowed to overlap, each x would need to explicitly be assigned to a single function definition.