Pre-Calculus - How do I write this in Interval Notation? PLEASE HELP! 10 POINTS FOR BEST ANSWER &THUMBS UP?

For the range: Y can be anything except between 0 and 1, but how would I write this in interval notation?

Also for the Domain: x cannot equal 1 and x cannot equal -1

For my answer I got (-infinity, -1) U (1,+infinity)

Is this right?

3 Answers

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  • Chris
    Lv 7
    8 years ago
    Favorite Answer

    If Y can be exactly zero or exactly 1 (i.e., the range that it cannot be is 0 through 1 non-inclusive), then the range in interval notation is:

    (-infinity, 0] U [1, +infinity)

    If Y cannot be exactly zero or exactly 1 (i.e., the range that it cannot be is 0 through 1 inclusive), then the range in interval notation is:

    (-infinity, 0) U (1, +infinity)

    For the domain, what you listed is not correct based on what you describe, because the X value can be anything between -1 and 1, just not exactly -1 or 1. The correct description for the domain is:

    (-infinity, -1) U (-1, 1) U (1, +infinity)

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  • Donna
    Lv 4
    4 years ago

    (x + 22) / (x + 2) >=5 {subtract 5 from each side} (x + 22) / (x + 2) - 5 >= 0 (now write 5 with a common denominator) (x + 22) / (x + 2) - 5(x +2) / (x + 2) >= 0 (combine) (x + 22 - 5(x + 2)) / (x + 2) >= 0 (simplify) (x + 22 - 5x - 10) / (x + 2) >= 0 (12 - 4x) / (x + 2) >= 0 this will be true either when both factors are positive or both are negative. Using sign charts or the fact that the corresponding parabola opens downward, this will be positive between the zeros (3 and -2) We can also include 3, since that makes it 0, but we do not include -2 because that makes the denominator 0. A very common mistake is to multiply both sides by x + 2 and work it that way; however, the sign of x + 2 is unknown, and if it's negative, the direction of the inequality must be reversed. (-2 , 3] <=== solution or, -2 < x <= 3 (confirmed graphically) (if the original inequality is just (x + 22) / (x + 2) > 5, then do not include 3 ==> (-2 , 3)

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  • 8 years ago

    I got your back :) You would have two equations - one for domain and range. Domain is all the x-values that the graph/equation uses, and range is all the y-values that the graph/equation uses.

    Domain: (-infinity, -1) U (1, infinity)

    I believe that's what you got :)

    Range: (-infinity, 0] U [1, infinity)

    You would use brackets, since Y can still BE 0 and 1, just not between.

    Good job and good luck!!

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