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Identify the domain and range of the following:

f(x) = 4-x^2, -5<x<-1
3/2x + 3/2, -1<x<3 (both "<" signs are actually less than or equal to)
x+3, 3<x<10 (x<10 is actually less than or equal to)

All three are in a set. I'd like to say that the domain is all real numbers greater than -5 and less than or equal to 10, but I'm not sure. Also, how do you find the range with these types of functions?

Thank you!

  • math -

    So the function is composed of three contiguous intervals each of which has its own range.
    The domain and range are the aggregate of the individual quantities.
    Your suggestion for the domain is correct.
    Work out the range for each of the three intervals and use the union operator ∪ to combine them if the ranges are disjoint.

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