precalc review/calc

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For the curve y=2^[sqrt(9-x2)], find the range of the function.

I think the range is [0,8] but I don't know why. Could you show me how to get to that answer? Thanks.

  • precalc review/calc -

    I assume you mean:

    y=2^[sqrt(9-x^2)]

    we do not want to take the sqrt of a negative number so domain is |x|<3
    or
    -3 < x < +3
    eg
    if x = -3 or + 3, y = 2^0 = 1
    if x = -1 or + 1, y = 2^sqrt 8 = 7.1
    if x = -2 or + 2, y = 2^sqrt 5 = 4.7
    if x = 0 , y = 2^3 = 8
    So
    I think the range of y is 1 to 8, not 0 to 8
    that corresponds to y between 0 and 8 so I agree with you

  • do NOT agree with you -

    Last sentence is a typo.

  • precalc review/calc -

    Thanks! So because the smallest and biggest numbers +/- 3 and the middle number 0 result in the smallest and largest y values, 1 and 8 respectively, the range is therefore [1, 8]. That makes sense. :D

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