Horizontal Asymptote?

Question

whats the diff between a vertical and a horizontal asymptote? do u use the same formula to find both or is there one for each?

how to i find the horizontal asymptote? example: y=x-3/2x+5 after dividing both, i get 1/2 r (-11/2)/2x+5 therefore, the answer is y=1/2 yes?

Answer 1

If the value of an expression approaches (limit) to a certain value when x goes to +/- infinity, then that is the horizontal.
in the example you just gave yes when x approaches to infinity the value of the expression goes to 1/2, you are right.

If when x takes on a certain value and makes the expression go to +/- infinity, now you have a vertical asymptote.
look at the exaple you gave, it approaches to infinity (from right to +inf, from the left to the -inf) when x=-5/2.
So, line x= -5/2 is the vertical asymptote.
I hope this helps.

Answer 2

A horizontal asymptote is a HORIZONTAL line that the graph approaches but never reaches.
A vertical asymptote is a VERTICAL line that the graph approaches but never reaches.
Example
y = 1/x for x > 0 is a curve than can be quickly sketched by giving x values 1/8,1/4,1/2,1,2,4,8,etc
The corresponding values for y are then:-
8,4,2,1,1/2,1/4,1/8, etc
This curve lies in the first quadrant and the horizontal axis is line y = 0, the x axis is horizontal asymptote
vertical axis is the line x = 0, the y axis is vertical asymptote.
Upon division,I obtain an expression for y:-
y = 1/2 - 11/ [4(x - (- 5/2 )]
This indicates x = - (5/2) as a VERTICAL asymptote and y-->1/2 as x-->(- 5/2)

Answer 3

You don't use the same formula, but you do use the same thinking.

In the original equation you want to find values of 'x' that make the equation "Blow Up". That is you want values of 'x' that make 'y' very, very large (i.e. infinite).

so if we have:

** i'm not sure which equation you mean:

y = x + 5 - 3/(2x)

y = x - 3/(2x +5) --> i'm going to use this to explain

The first value of x is (kind of obvious) if 2x+5=0, then we have division by zero and 'y' would skyrocket.

The other is not as obvious (only because seldom are we taught in school to look for it) but if 'x' goes to infinity 'y' again would skyrocket ( to infinity as well).

So we have identified to things to investigate:

2x+5 =0
and
x getting very very large (i.e. to infinity)

The SPECIFIC value x = -5/2 tells us this MUST be a vertical asymptote.

Lastly, if 'x' gets very very large, the term -3/(2x +5) would get very very small; and we could approximate y = x - 3/(2x +5) as simply y =x.

And that's it.

We have a verticle asymptote at x = -5/2 (SPECIFIC x value)
And the line y =x is an asymptote.

******************************
For the purely horizontal asymptote's you'll get something that looks like y =7.

Answer 4

vertical asympototes are vertical lines at some x value toward which the function approaches but never touches or crosses.

horizontal are similar at some y value toward which the function approaches but never touches or crosses.