Question

Could someone help me on this question please,

Find Vertical and Horizontal asymptotes:

f(x) = ( x-2 ) / ( 4 - l2x+1l )

Answer 1

for vertical asymtopes solve for the denominator = 0

Answer 2

Would limits be involved with this question? Like would I have to put lim x-> infinity or something?

Answer 3

for very large values of x the formula simplifies to x / -2x, or y=1/-2

Answer 4

not really

Answer 5

for very large negative values of x the formula simplifies to x/-(-2x) , or y=1/2

Answer 6

Oh okay, its just cause my teacher wants us to involve limits somehow :P

Answer 7

For vertical asymptotes take the limit at the points that cannot exist in the domain, for example
\[\lim_{x \rightarrow 4^-}\]
and
\[\lim_{x \rightarrow 4^+}\]

If 4 wasn't in the domain, if you get infinity you have an asymptote, if you get a regular number you have a hole

Secondly
for horizontal asymptotes
you just take the limit at infinity

\[\lim_{x \rightarrow infinity-}\]
and
\[\lim_{x \rightarrow infinity^+}\]

which should give you your horizontal asymptotes,
Two Cases

1. if the degree of the denominator leading term is larger than the numerator leading term, you should get zero by taking the limit (zero being your horizontal asymptote.
you have a horizontal asymptote at the point of the leading coefficients (the infinity should cancel out),

2. If you have a term with a denominator larger than the neumorator you should get a asympotote at zero

YOu have no asymptotes if the degree of the neumartory is larger than that of the denominator

Hope this helps