5) Use the properties of *continuity* to prove whether or not *h(x)* is continuous at *x* = 3. If *h(x)* is not continuous at *x* = 3, then state the type of discontinuity.

*h(x)* = {3*x*^{2} - 3 if *x *<* *3

* *{7*x* + 3 if *x* ≥ 3* *

GAMEMASTERX40 Mar 19, 2020

#1**+1 **

Hey, GM!!!!!.....good to see you !!!

Let x = 3

Then 3(3)^2 - 3 = 3 *9 - 3 = 27 -3 = 24

And 7(3) + 3 = 21 + 3 = 24

Note that the output is the same....so.....this piece-wise function is continuous at x = 3

CPhill Mar 19, 2020

#2**+1 **

Hi CPhill! It is good to see you too! Things have been complicated the last few weeks because of the virus that you may know and people are in quarantine to avoid contact but that won't stop me from learning. Can you also answer this question here, please? Thanks!

GAMEMASTERX40
Mar 19, 2020

edited by
GAMEMASTERX40
Mar 19, 2020

edited by GAMEMASTERX40 Mar 19, 2020

edited by GAMEMASTERX40 Mar 20, 2020

edited by GAMEMASTERX40 Mar 19, 2020

edited by GAMEMASTERX40 Mar 20, 2020