# Find the asymptotes of f(x)= x/square root(4x-1)

• m0286
In summary, the conversation revolved around finding the asymptotes of the function f(x)=x/square root(4x-1) and understanding how to approach the problem. The individual was stuck and asked for help, and eventually came to the conclusion that the vertical asymptote is x=1/4 and the horizontal asymptote is y=0. The conversation also touched upon the process for finding asymptotes and how to apply it in this particular case.
m0286
Hello,
Well I am 1 review question away from completing my calculus independent learning course WOOO! But I am stuck... can some one PLEASE HELP

Find the asymptotes of f(x)= x/square root(4x-1)
THANKS SO MUCH YOU GUYS HAVE BEEN AWESOME!

What is an asymptote?
(I know; but show that you have thought a bit upon the problem)

sorry, i showed my work now.

Sorry I know what an asymptote is, i just didnt want to type it all out sorry I guess i should have..
I know a vertical asymptote is a vertical line on the graph that the function comes closer and closer to but never touched, and horizontal is the same thing but a horizontal line.

I know for vertical asymptotes if its written in the form y=f(x) you can make the denominator =0 and figure it out from there.. and I understand doing that however not really witha square root? Would it just be 4x-1=0, x=1/4? and that's the vertical asymptote, or does the square root play more in that?

For horizontal asymptotes, i know you make it so
lim x/sqare root(4x-1)
x->infinity
Then you divide all parts by the highest power of x. so i know x/x is 1 so it would be 1/square root(4x-1) This I am not sure about now.. how do i divide square root (4x-1) by x? does the square root matter or would it be 4x/x-1/x which is 1/4-0, which is 1/4 as the horizonatl asymptote?

THANKS!

you are thinking right i guess...
For horizontal asymptote it will be y=0and for vertical it will be x=1/4 as per definitions

## What are the asymptotes of f(x)= x/square root(4x-1)?

The asymptotes of f(x)= x/square root(4x-1) are the lines that the graph of the function approaches but never crosses.

## What is the vertical asymptote of f(x)= x/square root(4x-1)?

The vertical asymptote of f(x)= x/square root(4x-1) is x=1/4. This is because the denominator of the function becomes 0 at x=1/4, and dividing by 0 is undefined.

## What is the horizontal asymptote of f(x)= x/square root(4x-1)?

The horizontal asymptote of f(x)= x/square root(4x-1) is y=0. This is because as x approaches positive or negative infinity, the square root term becomes much larger than the x term and the function approaches 0.

## Is there a slant asymptote for f(x)= x/square root(4x-1)?

No, there is no slant asymptote for f(x)= x/square root(4x-1). A slant asymptote occurs when the degree of the numerator is one more than the degree of the denominator, but in this case, both have a degree of 1.

## How do you graph f(x)= x/square root(4x-1) and its asymptotes?

To graph f(x)= x/square root(4x-1), plot points for various x values, making sure to exclude x=1/4 to avoid the vertical asymptote. Then, draw a smooth curve connecting the points. To graph the asymptotes, draw a dotted line at x=1/4 for the vertical asymptote, and a straight line at y=0 for the horizontal asymptote.

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