Why is there no y intercept in (x+2)/(x^2-2x)?

Question

anonymous · Answer

Because there is a vertical asymptote there.

anonymous · Answer

ok i see..but if i plug in 0 for x, is the reason it doesnt work because it would be 2/0 which isnt real so its just none?

tkhunny · Answer

x = 0 is not in the Domain.  It is generally considered inappropriate for the denominator of any expression to be zero (0).  Please do NOT simply substitute x = 0.  It's not in the Domain,  Resist the evil.

anonymous · Answer

is that just because of the x^2??

anonymous · Answer

i just need a simpler way to know there is no y intercept without looking at the asymptotes

anonymous · Answer

No, its because the parent function, 1/x represents that.

anonymous · Answer

i dont understand. what do i need to do to find the intercept or realize there is none? it seems too complicated

tkhunny · Answer

If you examine this function, Q(x) = x^2 - x, you will see that Q(x) takes on the value zero (0) for x = 0 and for x = 1.  Thus, Q(x) is not suitable for a denominator for these two values.  Take them out of the Domain and you are good.  That is one thing that vertical asymptotes do - remove values from the Domain.

anonymous · Answer

How does my vertical asymptote of x=0 and x=2 affect  my y intercept at all?

anonymous · Answer

Can't there still be one?

tkhunny · Answer

If you have x = 0 as a Vertical Asymptote, you should notice that x = 0 IS the y-axis.  Since the y-axis is NOT in the Domain, there is NO y-intercept.  Any other vertical asymptote does not cause the same conclusion.  Only x = 0 (the y-axis).

anonymous · Answer

So if x=0 was not my v.a., i would still have an intercept for y by plugging in 0 for x? Can i do that now since x=0 is not restricted?

tkhunny · Answer

First, you really have to get away frotm the term "plug in".  It is not well-defined and often confusing.

If x = 0 is in the Domain, you most certainly may substitute x = 0 into your function and determine the corresponding y-value, which, for x = 0, will be the y-intercept.

I think you have it!

anonymous · Answer

ok thank you so much!! pluggin in zero is just what ive been doing for forever

tkhunny · Answer

Well, quit it!  :-)