Finding the range for a piecewise function

[gloomygoldfish]

I am to find the range of this piecewise function:
f(x)= 1/2 x² if x<1
4x-2 if x>1

I am unsure how to even begin this problem. Any help would be appreciated. Thanks!

 

[tkhunny]

I am unsure how to even begin this problem.

I absolutely do not believe this. This is the first thing you need to get through this one, a little hope and maybe an adventurous spirit.

Defintion of "Range" is what?

The Range of y = x is All Real Number, since for any y selected from the real numbers, there is an x that will get you there with this relationship.

The Range of y = x^2 is all nonnegative Real Numbers. You can't get any negative ones. Said another way, for any y selected from the nonnegative real numbers, there is at least one x that will get you there. Also, for any negative Real number, there is no x that will manage!

So, what values of f(x) can be produded? That is what you need to discover.