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# An Explanation Please???

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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

Mar 29, 2018

### Best Answer

#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. Mar 29, 2018
edited by Melody  Mar 29, 2018

### 3+0 Answers

#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. 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
edited by Melody  Mar 29, 2018
#3
0

Thank you very much I will think on this hard as suggested!

p.s. it's dom6547 not dom6527!

dom6547  Mar 29, 2018