@phi
State the vertical asymptote of the rational function.
$\large\dfrac{(x-6)(x+6)}{x^2-9}$

Question

@phi 
State the vertical asymptote of the rational function.
$\large\dfrac{(x-6)(x+6)}{x^2-9}$

imstuck · Answer

factor the bottom and see what you get.  THere are 2 of them.

phi · Answer

vertical asymptotes are caused by "dividing by zero"

any idea what x values cause the bottom to be zero?

sleepyjess · Answer

(x-3)(x+3)?

phi · Answer

that is how you can see more clearly what x values make the bottom zero.

sleepyjess · Answer

-3 and 3?

phi · Answer

if x is -3
then (x - 3) (x+3) turns into  (-3 -3) * (-3 + 3) =  -6*0 = 0
and similarly for x= 3,  we will get zero.

when x is -3 or 3, you will get an asymptope

sleepyjess · Answer

Ok so for vertical asymptotes I just need to factor the bottom and that will make it easy to find them?

phi · Answer

you can remember this if you remember
vertical asymptote means y "zooms up"
and to get big values for y ,  where y = top/bottom,  make the bottom *very tiny*
because dividing by a tiny number gives a big number.

sleepyjess · Answer

I have 2 more. Do you want me to put them here or open a new question?

phi · Answer

to find the vertical asymptotes you need to find when the bottom is zero.  that turns into the problem of  , for example,

a x^2 + b x + c = 0
i.e. solving a quadratic.

for bigger degrees it gets harder!

phi · Answer

if you post what you think the answer is.

sleepyjess · Answer

State the domain of the rational function.
$\large\dfrac{6}{4-x}$
All real numbers except 6.
All real numbers except 4.    $\Leftarrow$ I think this one
All real numbers except -6 and 6.
All real numbers except -4 and 4.

phi · Answer

yes.  all x's are ok except  when x is 4 (which causes a divide by zero , and we don't like dividing by zero)

sleepyjess · Answer

Give an example of a rational function that has no horizontal asymptote and a vertical asymptote at
x = 1.

This one I am thinking something like $\large\dfrac{x^3+2x-8}{x^2-1}$

phi · Answer

from the other post, we know it does not have a horizontal one (degree of top is 3 which is different from the degree of bottom 2)

and x= 1  will cause the bottom to be zero.  

sounds correct.

sleepyjess · Answer

Thank you so much! I wish I could give you more medals. $\Large\ddot\frown$

phi · Answer

I have lots of medals.  but thanks.