Is y=(x^3)+1 and Even or Odd Function???

Question

fibonaccichick666 · Answer

Can you tell me what it means for something to be even or odd?

fibonaccichick666 · Answer

What are the definitions of each term?

openstudy9 · Answer

Well, if a function is Even, than the negative of it is the same as the positive of it. If it is Odd, than $$-f(x)=f(-x)$$

openstudy9 · Answer

Is it Odd??

fibonaccichick666 · Answer

Good on definition, now, pick a convenient number, say x=1 and see which definition holds

openstudy9 · Answer

1^3 +1 is 2. (-1)^3 +1= 0 so not even,  1^3 +1 is 2, and -(1^3 +1) is -2. So the Answer is Neither!?

fibonaccichick666 · Answer

yep yep :)

openstudy9 · Answer

Thanks!!!

fibonaccichick666 · Answer

You just proved that it is not odd and that it is not even.

fibonaccichick666 · Answer

now, if it was only x^3 it would be a different story.  you would find that it is odd.  So if it is asking if the mother function is even or odd, it would be odd.

openstudy9 · Answer

Oh, I see!
THank YOU

fibonaccichick666 · Answer

wait hold on a sec.  One issue

fibonaccichick666 · Answer

I missed something in your work

fibonaccichick666 · Answer

I skimmed sorry.  
so here: "1^3 +1 is 2. (-1)^3 +1= 0 so not even,  1^3 +1 is 2, and $$\color\red{-(1^3 +1)}$$ is -2. So the Answer is Neither!?"
What is marked in red, isn't actually f(-x).  f(-x) is (-1)^3+1 when f(x) is 1^3+1

openstudy9 · Answer

OK