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Question 230026: Is the equation a function? Why or why not?
x^2+x^3+y=6x
I put it in slope-intercept form like so: y=6x-x^5
Also, is this a function, why or why not?:
y^2+2x-4=o
Thank you for your time
Found 2 solutions by rapaljer, solver91311:
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! 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
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
NO! NO! NO!  No how, no way. (x^3) = x^5) is a true statement. Also, you can't put a cubic into 'slope-intercept' form. Slope-intercept is a form of linear equation, and this is anything but linear.
Is it a function?
Well, it is a relation that maps values of  to values of  . The question is, is there any value of that maps to more than one value of ?
In general, all polynomial relations of the form:
 are functions.
Let's examine a graph of your relation:
The test to see if you have a function is the vertical line test. If you can find a vertical line that intersects the graph of the relation in more than one point, then you do NOT have a function. In the case of the given relation, there is no such vertical line, therefore the relation is, in fact, a function.
On the other hand,
Let's look at this graph:
Oops! Lots of vertical lines that intersect the graph in two places, in fact, there are an infinity of them. Also, there is only one vertical line that intersects the graph in exactly one point, and that would be the vertical line that is tangent to the curve at the vertex, the vertical line  .
So, NOT a function.
John
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