ganeshie8 one year ago Find the y intercepts of $\large y=\frac{3x^3-x}{x^2-4x}$

1. campbell_st

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

2. ganeshie8

Am i really allowed to let x = 0 here

3. kanwal32

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

4. campbell_st

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 $y = \frac{3\times0^2 - 1}{0 - 4}$

5. ganeshie8

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

6. campbell_st

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...

7. ganeshie8

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

8. campbell_st

here is my graph of the equation

9. ganeshie8

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

10. campbell_st

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

11. campbell_st

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

12. ganeshie8

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

13. ganeshie8

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

14. campbell_st

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

15. Anikate

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

16. anonymous

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?

17. anonymous

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

18. ganeshie8

then im convinced wolfram is lying about the y intercept

19. jigglypuff314

or perhaps some definition of a y intercept somewhere includes the limit?