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Math Help - help with Pre-Calc HW questions

  1. #1
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    Post help with Pre-Calc HW questions

    1). True or False. The graph r(x) = (2x-1)/(x+2)(x-1) changes signs at x = -2. Justify your answer.

    2). Which of the following is the solution to (1)/(x+2)^2 ≥ 0?
    a. (-2,∞)
    b. All x ≠ -2
    c. All x ≠ 2
    d. All real numbers
    e. There are no solutions

    3). Which of the following is the solution to (x^2-1)^2 ≤ 0?
    a. {-1,1}
    b. {1}
    c. [-1,1]
    d. [0,1]
    e. There are no solutions

    I appreciate any help on any or all questions.
    Thank you so much!
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  2. #2
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    True or False. The graph r(x) = (2x-1)/(x+2)(x-1) changes signs at x = -2. Justify your answer.

    complete a sign chart

    2). Which of the following is the solution to (1)/(x+2)^2 ≥ 0?
    a. (-2,∞)
    b. All x ≠ -2
    c. All x ≠ 2
    d. All real numbers
    e. There are no solutions

    use some common sense ... what can you say about the sign of 1/(x+2)^2 for all x except x = -2 ???

    3). Which of the following is the solution to (x^2-1)^2 ≤ 0?
    a. {-1,1}
    b. {1}
    c. [-1,1]
    d. [0,1]
    e. There are no solutions

    common sense again ... what is the sign of (x^2-1)^2 for all x except x = 1 and x = -1 ???
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  3. #3
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    Quote Originally Posted by skeeter View Post
    True or False. The graph r(x) = (2x-1)/(x+2)(x-1) changes signs at x = -2. Justify your answer.

    complete a sign chart

    2). Which of the following is the solution to (1)/(x+2)^2 ≥ 0?
    a. (-2,∞)
    b. All x ≠ -2
    c. All x ≠ 2
    d. All real numbers
    e. There are no solutions

    use some common sense ... what can you say about the sign of 1/(x+2)^2 for all x except x = -2 ???

    3). Which of the following is the solution to (x^2-1)^2 ≤ 0?
    a. {-1,1}
    b. {1}
    c. [-1,1]
    d. [0,1]
    e. There are no solutions

    common sense again ... what is the sign of (x^2-1)^2 for all x except x = 1 and x = -1 ???

    So.. number 2 is b, and number 3 is c?
    Is that correct?
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  4. #4
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    Quote Originally Posted by live_laugh_luv27 View Post
    So.. number 2 is b, and number 3 is c?
    Is that correct?
    yes ... no
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  5. #5
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    Quote Originally Posted by skeeter View Post
    yes ... no
    Is number 3 b? I don't really understand the notation...
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  6. #6
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    you're guessing ... go research the notation from your text.
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  7. #7
    Math Engineering Student
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    As for #3, the only way when x^2-1 be zero happens when x=1 or x=-1. Those numbers are unique 'cause (x^2-1)^2>0, hence the solution is \{-1,1\}. ( \{\cdot\} means the numbers you see, that's all; on the other hand [-1,1] means the numbers covered between -1 and 1, including them.)
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  8. #8
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    I know that [ ] is closed interval, quantity, and { } is set, or quantity, but I don't understand how that would relate to the exclusions of x ≠ 1,-1. Would it mean that the set {1,-1} is the solution to the equation? because x ≠ 1,-1?
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  9. #9
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    sorry, i meant {-1, 1}
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  10. #10
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    Thanks for your help
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