The graph of \(\frac{4(x+1)}{x(x-4)}\) has a x intercept at -1 (plugging in 0 for y agrees with this and the graph does). Yet since the bottom power is greater than the top power, shouldn't the horizontal asymptote be zero and not allow an x intercept?

Could you explain why??

do x intercepts just not follow the horizontal asymptote rule???

Here is the function's graph: https://www.desmos.com/calculator/ullbutopnh

-Thanks

dom6547
Mar 29, 2018

#2**+4 **

You have not quite graphed the given equation ChowMein.

dom6527,

You graph is correct.

AND The y value does approach 0 as \(x\rightarrow \pm \infty\)

However, you cannot divide by 0 which means that x cannot equal 0 or +4

There are vertical asymptotes when x =0 and when x=4

If -1

\(y=\frac{4(x+1)}{x(x-4)}\\ y=\frac{4(positive)}{neg*(negative)}\\ y=positive\)

BUT

if x<-1 then

\(If\;\; x<-1\\ y=\frac{4(x+1)}{x(x-4)}\\ y=\frac{4(negative)}{neg*(negative)}\\ y=negative\)

So the x axis has to be crossed at x=-1

I hope this helps but....

You probably need to think about it a lot.

Melody
Mar 29, 2018

#1**+1 **

A horizontal asymptote is the **line that a function approaches as x goes to infinity or negative infinity**. So although the function crosses the x axis at (-1, 0), it's not what the function approaches as x goes to infinity or negative infinity. It's why something like this could happen.

ChowMein
Mar 29, 2018

edited by
Guest
Mar 29, 2018

#2**+4 **

Best Answer

You have not quite graphed the given equation ChowMein.

dom6527,

You graph is correct.

AND The y value does approach 0 as \(x\rightarrow \pm \infty\)

However, you cannot divide by 0 which means that x cannot equal 0 or +4

There are vertical asymptotes when x =0 and when x=4

If -1

\(y=\frac{4(x+1)}{x(x-4)}\\ y=\frac{4(positive)}{neg*(negative)}\\ y=positive\)

BUT

if x<-1 then

\(If\;\; x<-1\\ y=\frac{4(x+1)}{x(x-4)}\\ y=\frac{4(negative)}{neg*(negative)}\\ y=negative\)

So the x axis has to be crossed at x=-1

I hope this helps but....

You probably need to think about it a lot.

Melody
Mar 29, 2018