pre calc help important!!

Question

anonymous · Answer

state the vertical asymptote of the rational function. f(x) = (x-3)(x+4)/x^2-1

solomonzelman · Answer

$\large\color{black}{  f(x)= \frac{\LARGE (x-3)(x+4)}{\LARGE x^2-1}   }$

solomonzelman · Answer

right?

anonymous · Answer

yes

solomonzelman · Answer

So, we are just doing a basic observation of the domain.
You know that:

$\large\color{black}{  x^2-1 \ne 0 }$ right?

anonymous · Answer

yes

solomonzelman · Answer

so what is the restriction for x. What x cannot equal?

anonymous · Answer

x can't equal 0?

solomonzelman · Answer

$\large\color{black}{   x^2-1=0  }$ solve for x.

anonymous · Answer

x^2=1

solomonzelman · Answer

and x is equal to?

anonymous · Answer

x=3 and x=-4

solomonzelman · Answer

wait,. if x^2=1, then x=?   (there are 2 solutions)

solomonzelman · Answer

these solutions are the vertical asymptotes.

solomonzelman · Answer

take the square root fo each side.

anonymous · Answer

what do you mean square root of each side why wouldn't the answer be 3 and -4?

solomonzelman · Answer

$\large\color{black}{    x^2-1 =0    }$
$\large\color{black}{    x^2=1        }$
$\large\color{black}{    x=?       }$

solomonzelman · Answer

(we are not finding when the function is a zero, we are finding the undefined values for the denominator)

anonymous · Answer

oh +/-1

solomonzelman · Answer

Yes.  $\large\color{black}{    \pm 1     }$

anonymous · Answer

thanks! can u help me with 1 more problem

solomonzelman · Answer

So your vertical asymptotes are:
$\large\color{black}{   x=1   }$  and  $\large\color{black}{    x=-1  }$

solomonzelman · Answer

I can try;)

solomonzelman · Answer

but in a different question.

anonymous · Answer

why a different one? why not just on here

solomonzelman · Answer

Well, I don't mind, but the rules of this website are that you can ask as many questions as you need, but you should ask one question per post.

solomonzelman · Answer

One reason I can think of, is thta the thread shouldn't have a very slow loading time.

solomonzelman · Answer

you can ask it here for now though

anonymous · Answer

State the horizontal asymptote of the rational function.
f(x) = x+9/x^2+2x+3

solomonzelman · Answer

anonymous · Answer

i'm solving for y

solomonzelman · Answer

I think it is just y=0, if any horizontal asymptote.

solomonzelman · Answer

I meant y initially, but wrote x-:(

anonymous · Answer

oh ok. the answer choices are 
y = x
 None
 y = 0
 y = 9

solomonzelman · Answer

y=0 seems to be it

anonymous · Answer

ok thanks