## znimon 3 years ago How do I find the domain of this function?

1. znimon

$g(x) \sqrt{x^2 - 3x - 40}$

2. znimon

I have $\sqrt{(x-8)(x+5)}$

3. znimon

$(x-8)(x+5) \ge 0$

4. znimon

The original problem is at the top.

5. Yahoo!

Draw a number line and see for it

6. znimon

I don't know what x can't be though

7. znimon

I know the answer but I don't know how to get the answer.

8. Yahoo!

(-infinity , 5] U [8 , infinity)

9. znimon

yeah but how do I find that?

10. Yahoo!

just do trial and error method...)

11. Yahoo!

(x−8)(x+5)≥0

12. Yahoo!

luk for the vlue of x which satisfies this...

13. znimon

There must be a logical way to find the answer, right?

14. ganeshie8

(x-8)(x+5) >= 0 its a parabola, right ?

15. znimon

I could input it into my graphing calculator but other wise I don't know how to tell if its a parabola or not.

16. ganeshie8

y = ax^2 + bx + c is a parabola

17. ganeshie8

any quadratic function gives a parabola graph

18. znimon

ok

19. ganeshie8

can you find the x intercepts ?

20. ganeshie8

once you find x-intercepts, you would know where the parabola dips into x axis (goes negative)

21. ganeshie8

|dw:1346519548989:dw|

22. znimon

Oh ya that would be the point at which the g(x) function is 0, so its x - 8 = 0, x = 8, x+ 5 = 0, x=-5, and since its a parabola the graph only passes through zero twice. Nice dude, so the domain is (-infinity, -5] U [8, +infinity]

23. ganeshie8

yeah nice you got it :)

24. znimon

@ganeshie8

25. znimon

Awesome, thanks again. Is there a way I could recognize any graph's shape or at least some and would you recommend memorizing those?

26. ganeshie8

if the degree is 2, then its a parabola

27. ganeshie8

finding domains for other polynomials is bit tricky... as they may dip into x-axis multiple times

28. znimon

okay

29. ganeshie8

do you knw sketching polynomilas (end behiavior thingy )

30. znimon

never heard of it

31. ganeshie8

end behavior helps you sketch ANY polynomial freehand

32. znimon

Thanks dude, I'll look it up

33. ganeshie8

process is basically : 1) find x intercepts 2) using end-behavior sketch the graph by hand

34. ganeshie8

its easy concept and worth learning... im sure you wil get hang of it in few minutes....... good luck :)

35. znimon

why is it that a polynomial with a degree of two is a parabola?

36. znimon

Thanks again.

37. ganeshie8

uhh il have to think...... idk exactly... i think it has something to do with local maximum/minimum + increasing/decreasing thingy. we need to turn to calculus for proper understanding. im also learning... . so im no good for answering this :(

38. ganeshie8

@mukushla @eliassaab @experimentX

39. znimon

Oh, I have enough to learn for now so it doesn't matter to me. I bet I wouldn't understand the explanation if it involves terms I've never had before haha.