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anonymous

  • one year ago

f(x) = 10 x^2-9 find domain and range

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  1. DanJS
    • one year ago
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    are there any values for x that won't work?

  2. anonymous
    • one year ago
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    9?

  3. anonymous
    • one year ago
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    sorry i have no idea on where to start

  4. DanJS
    • one year ago
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    nah, x=9 will return a value for f(x) THe domain is all the input values that work the range is the values f(x) takes

  5. DanJS
    • one year ago
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    For x^2, any real value will work, right

  6. anonymous
    • one year ago
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    right

  7. DanJS
    • one year ago
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    THe parabola opens in the vertical direction, it gets wider and wider forever, the values for x can be any real value That is the domain

  8. anonymous
    • one year ago
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    so its infinity?

  9. DanJS
    • one year ago
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    -infinity to +infinity

  10. jdoe0001
    • one year ago
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    \(\Large (-\infty,+\infty)\)

  11. DanJS
    • one year ago
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    THe domain of f is all values for x, such that, x is an element of the reals

  12. anonymous
    • one year ago
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    so the range would also be (infinity,-infinity)

  13. DanJS
    • one year ago
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    hmm, look at the function. x^2 is the only variable, x^2 will always be posistive or zero

  14. jdoe0001
    • one year ago
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    he's referring to the domain ony thus far =) \(\large \{x|\quad x\in \mathbb{R}\}\)

  15. DanJS
    • one year ago
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    how does that affect what values f(x) can take

  16. anonymous
    • one year ago
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    so x would be 9?

  17. DanJS
    • one year ago
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    no x will be any real number, from the domain we just figured f(x) may be limited to some interval(s) sometimes, depending on the nature of the function

  18. DanJS
    • one year ago
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    If x^2 is 0 or larger, how does that limit the values for f(x) ?

  19. DanJS
    • one year ago
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    something squared will be positive, (-1)^2 = -1 * -1 = +1

  20. DanJS
    • one year ago
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    To graph this parabola, you probably will figure the vertex point, and the + on the ax^2 term means it opens toward the +y direction

  21. anonymous
    • one year ago
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    right I got the graph

  22. DanJS
    • one year ago
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    if x^2 is always 0 or larger, the smallest value for f(x) is when x = 0 , and f(x) = -9, and the thing opens towards positive y. the values for f(x), THE RANGE , is then limited to y values greater than or equal to -9

  23. anonymous
    • one year ago
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    so in interval notation would it look like (-9,infinity)

  24. DanJS
    • one year ago
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    bra-ket for the -9, it can be that value

  25. DanJS
    • one year ago
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    greater than or equal to -9

  26. DanJS
    • one year ago
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    [-9 , inf)

  27. anonymous
    • one year ago
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    oh my gosh, okay thank you, im starting to get it now

  28. DanJS
    • one year ago
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    welcome, takes practicing

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