Question 230026
First of all NEVER combine unlike terms!!  x^2 + x^3 CANNOT be combined!


In answering your question, since you CAN solve for y in terms of x, such that for EACH value of x, there is a UNIQUE value of y, then it IS a function.


The equation with a y^2 is NOT a function, since you CANNOT solve for y in terms of x where each x value gives a unique y value.  If you did solve for y, it would be y= Plus or Minus something, which is NOT a function.


For my NON-TRADITIONAL explanation of FUNCTIONS, please see my own website.  Do a "Bing" or "Google" search for my last name "Rapalje".  Near the top of the search list, look for "Rapalje Homepage".  Near the top of the Homepage, look for "MATH IN LIVING COLOR", select "COLLEGE ALGEBRA", and in Chapter 2, look for the topic "Functions, Domain, and Range".  The explanation is in COLOR, which I think helps.


In addition, I have two FREE videos on "Functions, Domain, and Range" on my website.  From my Homepage, look for "Rapalje Videos in Living Color" and select either Intermediate or College Algebra (depending upon your level of understanding!).  I apologize that these videos are a few years old, and I did NOT make use of graphing calculators.  Nevertheless, the price is right--they are free!  You may need to download RealPlayer if you don't already have it, but this is free also.


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus