HELP !! Answer the questions shown

For a function to be continuous at an x-value of -3 you need to make sure two things line up:

First, we need to show that the limit from the left equals the limit from the right.

Second, we need to show that this limit equals the functions value.

The left hand limit involves the first piece, f(x) = x^2 - 9:

The right hand limit invovles the second piece, f(x) = 0:

Since the two one-sided limits do match, we can just say:

(no one-sided pieces needed now)

So that was step #1, to make sure the limit exists.  Next we need to make sure the limit is headed to the same place where the functions.  Since we're using x=-3, we'll use the top piece of the function because x=-3 fits with that piece ( x ≤ -3 ).

From this, we know that , so the function is continuous at -3.  (We also know parabolas and lines are continuous in general, so we only needed to check where the two pieces came together at x = -3.)

the f

last graph i believe

step-by-step explanation:

worked it out i believe