Find the y intercepts of $$\large y=\frac{3x^3-x}{x^2-4x}$$

Question

campbell_st · Answer

so for the y, intercept, don't you let x = 0

but factor out x 1st 

$$y = \frac{x(3x^2 - 1)}{x(x - 4)}$$

ganeshie8 · Answer

Am i really allowed to let x = 0 here

kanwal32 · Answer

3x^2-y(x-4)-1 and putting d>0

campbell_st · Answer

well if you factor out x you get 

$$y=\frac{3x^2 -1}{x - 4}$$

and to find the y-intercept for any curve... its a case of letting x = 0

so 

$$y = \frac{3\times0^2 - 1}{0 - 4}$$

ganeshie8 · Answer

don't we need to worry about the fact that x=0 is not part of the domain

campbell_st · Answer

x = 0 would be a point of discontinuity the way I read the question and work on the solution. 

lol... now I see your point...

ganeshie8 · Answer

Haha mother wolfram also says (0, 1/4) is the y intercept http://www.wolframalpha.com/input/?i=y+intercepts+%283x%5E3-x%29%2F%28x%5E2-4x%29

campbell_st · Answer

here is my graph of the equation

ganeshie8 · Answer

It is a point discontinuity, should not be part of the domain

campbell_st · Answer

so then the curve doesn't have a y-intercept as its discontinuous at that point

campbell_st · Answer

I'm only in high school... so they may do other things at university

ganeshie8 · Answer

Exactly! there should not be any y intercepts for this curve but idk what wolfram is thinking lol

ganeshie8 · Answer

Your graphing calculator is correctly saying (0, 1/4) is a point discont

campbell_st · Answer

I'm in Australia and some people, I think from the US seem to not consider a point discontinuity

anyway... glad you have a solution

anikate · Answer

lol this is confusing, I'll just have my teacher explain it to me tomorrow

anonymous · Answer

Yet at the same time wolfram tells us the obvious domain http://www.wolframalpha.com/input/?i=domain+%283x^3-x%29%2F%28x^2-4x%29 Wolfram contradicts itself?

anonymous · Answer

I think after simplifying we can not let $x=0$ and the graph of the function must be|dw:1434357482874:dw|