Question

Given f(x)=(3x+5)/(2x-6) find:
a) domain, in interval notation
b) vertical asymptote(s) if any:
c)horizontal asymptote if there is one:
thanks your help is very appreciated!

Answer 1

Do you mean (3x+5)/(2x-6)?

Answer 2

yes

Answer 3

a) we know that we can't divide something by 0, hence 2x-6 can't be 0, which means x can't be 3. Therefore, the domain of x is (-infinity, 3) U (3, infinity)

Answer 4

b) To determine the vertical asymptotes of any given function, we first find at which x value the function does not exist. By looking at the domain we know when x=3, the function does not exist.

We now need to test if x=3 is truly an asymptote (which means the limit as x approaches 3 is infinity or -infinity)

\[\lim_{x \rightarrow 3+} \frac{ (3x+5) }{ (2x-6) } = \infty\]
\[\lim_{x \rightarrow 3-} \frac{ (3x+5) }{ (2x-6) } = -\infty\]
x=3 is indeed an asymptote.

Answer 5

i understand those two....and thank you for taking the time to explain it. i wish i could give you a 100 metals

Answer 6

are you having trouble explaining it

Answer 7

c) To see the horizontal asymptote of any given function, we check when the x goes to infinity or -infinity, the y 'stops' at one value.

\[\lim_{x \rightarrow -\infty}\frac{ 3x+5 }{ 2x-6 } = \frac{ 3 }{ 2 }\]
\[\lim_{x \rightarrow \infty}\frac{ 3x+5 }{ 2x-6 } = \frac{ 3 }{ 2 }\]

Hence the horizontal asymptote is y=3/2

Answer 8

ok that makes sense... thanks a bunch

Answer 9

np :)