Before beginning the evaluations here let's think that we're using different letters for the function & variable than the ones which we've used to this point. That won't vary how the evaluation works. Do not get so much locked into seeing f for the function & x for the variable which you can't do any difficulty which doesn't have those letters.
Now, to do evaluations the first thing that we have to do is determine which inequality the number satisfies, and this will only satisfy a single inequality. While we determine which inequality the number satisfies we employ the equation related with that inequality.
In this question -6 satisfies the top inequality and hence we'll employ the top equation for this evaluation.
g( -6) = 3( -6)2 + 4 = 112
However, Piecewise functions do not arise all that frequently in an Algebra class, the do arise in various places in later classes and thus it is significant for you to understand them if you are going to be moving on to more math classes.
As a final topic we need to come back and touch on the fact that we can't always plug every x in every function. We briefly talked about this while we gave the definition of the function and we saw an example of this while we were evaluating functions. Now we need to look at this in a little more detail.
First we have to get a couple of definitions out of the way.