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Math Help - Domain and range (check my answers)

  1. #1
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    Post Domain and range (check my answers)

    1) y=5x-4
    D:all real no.
    R:all real no.

    2) y=-x^2+7
    D:all real no.
    R:all real no.

    3)  y=\frac{5-x}{x-2}
    D:all real no. except 2
    R: all real no.

    4)  y=\sqrt{4-x}
    D:x<=4
    R:all real no.

    5)  y=\sqrt{x^2-16}
    D:-5<=x>=5
    R:all real no.

    6)  y=\sqrt{4-x^2}
    D:-2<=x<=2
    R:0<=y<=2

    7)  y=\sqrt{x^2-1}
    D:-1<=x>=1
    R: all real no.

    8)  y=^3\sqrt{x}-x
    D:all real no.
    R:all real no.

    9)  y=\frac{1}{x}
    D:all real no. except zero
    R:all real no. except zero

    10)  y=\frac{x}{x-2}
    D:x not = 2
    R:y not = 1

    (If any are wrong tell me which one and try solving it for me )
    Thank you
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  2. #2
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    Quote Originally Posted by mj.alawami View Post
    1) y=5x-4
    D:all real no. Correct
    R:all real no. Correct

    2) y=-x^2+7
    D:all real no. Correct
    R:all real no. Incorrect

    3)  y=\frac{5-x}{x-2}
    D:all real no. except 2 Correct
    R: all real no. Incorrect

    4)  y=\sqrt{4-x}
    D:x<=4 Correct
    R:all real no. Correct

    5)  y=\sqrt{x^2-16}
    D:-5<=x>=5 Incorrect
    R:all real no. Incorrect

    6)  y=\sqrt{4-x^2}
    D:-2<=x<=2 Correct
    R:0<=y<=2 Incorrect

    7)  y=\sqrt{x^2-1}
    D:-1<=x>=1 Correct
    R: all real no. Correct

    8)  y=^3\sqrt{x}-x
    D:all real no. Correct
    R:all real no. Correct

    9)  y=\frac{1}{x}
    D:all real no. except zero Correct
    R:all real no. except zero Correct

    10)  y=\frac{x}{x-2}
    D:x not = 2 Correct
    R:y not = 1 Incorrect

    (If any are wrong tell me which one and try solving it for me )
    Thank you
    Have a go at fixing up these
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  3. #3
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    Some corrections (in blue) to the corrections:

    Quote Originally Posted by mj.alawami View Post
    1) y=5x-4
    D:all real no. Correct
    R:all real no. Correct

    2) y=-x^2+7
    D:all real no. Correct
    R:all real no. Incorrect

    3)  y=\frac{5-x}{x-2}
    D:all real no. except 2 Correct
    R: all real no. Incorrect

    4)  y=\sqrt{4-x}
    D:x<=4 Correct
    R:all real no. Correct Mr F says: The answer is incorrect. Draw the graph (it's the upper branch of a sideways parabola) ....

    5)  y=\sqrt{x^2-16}
    D:-5<=x>=5 Incorrect
    R:all real no. Incorrect

    6)  y=\sqrt{4-x^2}
    D:-2<=x<=2 Correct
    R:0<=y<=2 Incorrect Mr F says: The answer is correct. It's a semi-circle (upper half) of radius 2.

    7)  y=\sqrt{x^2-1}
    D:-1<=x>=1 Correct Mr F says: The blue inequality is pointing the wrong way.
    R: all real no. Correct

    8)  y=^3\sqrt{x}-x
    D:all real no. Correct
    R:all real no. Correct

    9)  y=\frac{1}{x}
    D:all real no. except zero Correct
    R:all real no. except zero Correct

    10)  y=\frac{x}{x-2}
    D:x not = 2 Correct
    R:y not = 1 Incorrect Mr F says: The given answer is correct. It's a hyperbola with horizontal asymptote y = 1 and vertical asymptote x = 2.

    (If any are wrong tell me which one and try solving it for me )
    Thank you
    Quote Originally Posted by Prove It View Post
    Have a go at fixing up these
    ..
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  4. #4
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    Quote Originally Posted by mr fantastic View Post
    Some corrections (in blue) to the corrections:



    ..
    When I was trying to find the ranges, I checked the domains of the inverse functions. I stupidly forgot that the functions needed to be one-to-one to have inverses.
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