Question

Which function has the following characteristics?

A vertical asymptote at x = 3
A horizontal asymptote y = 2
Domain: {x =/ +-3} (plus and minus 3)

A. y= (2x-8)/(x-3)
B. y=(x^2-9)/(x^2-4)
C. y= (2x^2-18)/(x^2-4)
D. y= (2x^2-8)/(x^2-9)

Im thinking it's either A. or D. just not sure?

Can someone please help me find the answer.

Answer 1

It's a, because when you have a vertical asymptote, you look at the denominator. Then you make the denominator equal to 0. So for a, the denominator is x-3.

x-3=0

just do algebra and isolate x.



For the y range you can plug into your graphing calculator and see when y almost, but doesn't touch 2. However I will present you the equation way.

First you choose the biggest exponents of x
\[\frac{ 2x-8}{ x-3 }\]
The biggest exponents are: 2x and 1x-3 and -8) don't count, they are not coefficients to x.

So...

2x/1x = 2 (Because x's cancel!)

So for this horizontal asymptote, you express this as: y = 2.

So A. Is your answer. :)

Answer 2

ok thanks because i found out that a. had a vertical asymptote of 3, a horizontal asymptote of 2 and the domain was x=/3. Then for d. i found out that it had a vertical asymptote of + - 3 horizontal asymptote of 2 and domain of x=+-3. The part where I got confused was where it said the Domain: {x =/ +-3} and A. did not have that option.

Answer 3

ahhh, I see, it means that on the screen shot, it means X cannot equal to POSITIVE or NEGATIVE 3 :D, so if you look at the graph on both negative and positive quadrant (for x) you can see this. Hope this helped you understand more ;p

Answer 4

you seen my attachment? I see it is saying that it does not equal to either positive or negative where as a is x=/ 3 so it still makes it A.

Answer 5

I think im starting to see it thanks for your help and time so I guess A. it is!

Answer 6

Yeah thats the thing, so on a graphing calculator the doman \[x \neq-3\]

would look something like this:



So the vertical asymptote is when a value can't touch a certain value of x. In this case, it follows the domain because you can see that x cannot equal to either positive or negative 3. In this case, the vertical asymptote does not touch +3. So it follows the domain that x cannot equal to positive or negative x.