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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    hey. do you mean f(x) = x / (15x^2 + 13x - 20) ?

  2. anonymous
    • 5 years ago
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    yes

  3. anonymous
    • 5 years ago
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    nevermind i solved it thanks

  4. anonymous
    • 5 years ago
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    i meant to ask a different question, sorry

  5. anonymous
    • 5 years ago
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    is there another question you want to ask?

  6. anonymous
    • 5 years ago
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    yes. it was determine domain and range using interval notation of f(x)= radicand(x^2 -8x -9

  7. anonymous
    • 5 years ago
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    \[f(x) = \sqrt{x^2 -8x -9}\]

  8. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    ok i understand so far

  11. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    yes, i have x=-9 and x=1

  13. anonymous
    • 5 years ago
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    that's not quite right, look at it again

  14. anonymous
    • 5 years ago
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    is it 9 and -1 instead?

  15. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    you still here, is this helping?

  20. anonymous
    • 5 years ago
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    im here thank you. how do you know what sign to use when determining if the equation is true?

  21. anonymous
    • 5 years ago
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    what i mean is, you plug in -2 to the equation to see if its true right?

  22. anonymous
    • 5 years ago
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    what do you mean by true?

  23. anonymous
    • 5 years ago
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    (-2)^2 - 8(-2) -9=0 ?

  24. anonymous
    • 5 years ago
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    or do you use an equality sign

  25. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    that's what the factoring is for

  27. anonymous
    • 5 years ago
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    by plugging in -2, we just want to see if that section of x-values comes up negative for y or positive

  28. anonymous
    • 5 years ago
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    oh ok

  29. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    so by plugging in -2, we get 11. then what from there?

  31. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    yes

  33. anonymous
    • 5 years ago
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    so since they're both positive, that means what for interval notation?

  34. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    but we still have to check the other intervals

  36. anonymous
    • 5 years ago
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    the one in the middle comes out negative

  37. anonymous
    • 5 years ago
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    and the last one comes out positive

  38. anonymous
    • 5 years ago
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    yes that's right, so the domain is the positive part

  39. anonymous
    • 5 years ago
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    ok so what does it look like in interval form?

  40. anonymous
    • 5 years ago
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    ok (-inf, -1) U (9, inf) is what it will be

  41. anonymous
    • 5 years ago
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    (-infinity,-1] [9,infinity)? something like that?

  42. anonymous
    • 5 years ago
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    no, you're right

  43. anonymous
    • 5 years ago
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    the brackets are right. (-inf, -1] U [9, inf) the U stands for union

  44. anonymous
    • 5 years ago
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    got it! thank you for your help!

  45. anonymous
    • 5 years ago
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    :)

  46. anonymous
    • 5 years ago
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    no problem.

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