Can some one help me with asymptotes, removable discontinuities, and intercepts? ;c
4 problems~

Question

Can some one help me with asymptotes, removable discontinuities, and intercepts? ;c 
4 problems~

ria23 · Answer

$$d(x)=\frac{ x^{2}-12x+20 }{ 3x }$$

ria23 · Answer

If I can get walked through a couple, I can do the others... I would appreciate the help... c:

anonymous · Answer

no removable discontinuity here, because noting cancels

jhannybean · Answer

First factor the op

jhannybean · Answer

top*

jhannybean · Answer

Once the top is factored, if there are any like terms you can cancel out, you can take those as your removable discontinuities.

anonymous · Answer

the degree of the top is larger than the degree of the bottom, so no horizontal asymptote either, although there will be a slant asymptote

jhannybean · Answer

Oh I forgot about those.... haha

anonymous · Answer

@Jhannybean  the numerator will not have a factor of $x$ so nothing will cancel

jhannybean · Answer

true true.

anonymous · Answer

vertical asymptote, set the denominator equal to zero and solve (in no steps, you get $x=0$ instantly)

anonymous · Answer

since the vertical asymptote is $x=0$ aka the y axis, there is no y intercept

anonymous · Answer

to find the x intercepts, solve 
$$x^2-12x+20=0$$ since a fraction is only zero if the numerator is 
complete the square or use the quadratic formula, this one does not factor over the integers

anonymous · Answer

i think that completes this one
are the steps more or less clear?

ria23 · Answer

Uhm... Haha, slightly confused...
So, to find the RD's, yhu'd just factor out the numerator, and whatever cancels is my answer..?
Asymptote's I set the denominator to 0
and the intercepts... I use the quadratic formula? 
Did I get it?

anonymous · Answer

So, to find the RD's, yhu'd just factor out the numerator, and whatever cancels is my answer..?
yes, in this case nothing cancels

anonymous · Answer

Asymptote's I set the denominator to 0
yes for the VERTICAL asymptote, not the horizontal one

ria23 · Answer

How would I find the horizontal?

anonymous · Answer

and the intercepts... I use the quadratic formula? 
yes of the numerator is quadratic'
you set the numerator equal to zero and solve, however you need to do it
if it was say just $x-1$ then the x intercept would be at $x=1$

anonymous · Answer

horizontal asymptote
there are three cases to consider 
ready?

anonymous · Answer

this is where you say "yes"

ria23 · Answer

Yes, haha. I'm sorry, my laptop crashed.

ria23 · Answer

@satellite73