## anonymous 5 years ago How do I: Express the domain of the given function using interval notation? f(x)=x/ 15x^2 + 13x - 20

1. anonymous

hey. do you mean f(x) = x / (15x^2 + 13x - 20) ?

2. anonymous

yes

3. anonymous

nevermind i solved it thanks

4. anonymous

i meant to ask a different question, sorry

5. anonymous

is there another question you want to ask?

6. anonymous

yes. it was determine domain and range using interval notation of f(x)= radicand(x^2 -8x -9

7. anonymous

$f(x) = \sqrt{x^2 -8x -9}$

8. anonymous

just so you know i believe radicand refers to what is under the square root, but you mean square root of (x^2 -8x -9) right?

9. anonymous

ok well for a square root function what you need to know is that what's under the square root can't be negative, because no real number multiplied by itself equals a negative

10. anonymous

ok i understand so far

11. anonymous

ok, so you want to try to factor that, to see where it is negative and where it is positive. you did the other problem so you know how to factor, right?

12. anonymous

yes, i have x=-9 and x=1

13. anonymous

that's not quite right, look at it again

14. anonymous

is it 9 and -1 instead?

15. anonymous

sorry, my browser crashed. yes, that's right. so you have sqrt ((x-9)(x+1)). what i like to do is draw a number line below that to help me see where the function is 0, negative, and positive

16. anonymous

so draw a line, hashmarks at -1 and 9, and we know it's 0 at those points, so mark 0 above -1 and 9

17. anonymous

now test a point on the left side, in the middle, and on the right to see if it comes up positive or negative

18. anonymous

try x= -2. (-2-9)(-2+1) is a negative times a negative, so that's positive. so now i mark all +++ to the left of the first 0 on my line

19. anonymous

you still here, is this helping?

20. anonymous

im here thank you. how do you know what sign to use when determining if the equation is true?

21. anonymous

what i mean is, you plug in -2 to the equation to see if its true right?

22. anonymous

what do you mean by true?

23. anonymous

(-2)^2 - 8(-2) -9=0 ?

24. anonymous

or do you use an equality sign

25. anonymous

no, we already know that the values that make what's under the square root equal to 0 are x = -1 and x = 9

26. anonymous

that's what the factoring is for

27. anonymous

by plugging in -2, we just want to see if that section of x-values comes up negative for y or positive

28. anonymous

oh ok

29. anonymous

remember the goal is to see which x-values make what's under the square root negative, because those are not part of the domain

30. anonymous

so by plugging in -2, we get 11. then what from there?

31. anonymous

it doesn't matter what the number is, we just care that it's positive, so did you draw the number line like i said? do you understand what i mean by that?

32. anonymous

yes

33. anonymous

so since they're both positive, that means what for interval notation?

34. anonymous

well -2 turned out positive, so that means that all values less than -1 turn out positive, so those will be part of the domain

35. anonymous

but we still have to check the other intervals

36. anonymous

the one in the middle comes out negative

37. anonymous

and the last one comes out positive

38. anonymous

yes that's right, so the domain is the positive part

39. anonymous

ok so what does it look like in interval form?

40. anonymous

ok (-inf, -1) U (9, inf) is what it will be

41. anonymous

(-infinity,-1] [9,infinity)? something like that?

42. anonymous

no, you're right

43. anonymous

the brackets are right. (-inf, -1] U [9, inf) the U stands for union

44. anonymous

got it! thank you for your help!

45. anonymous

:)

46. anonymous

no problem.