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Math Help - possible flow of solution of the equation

  1. #1
    rcs
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    possible flow of solution of the equation

    what is the domain, range, intercepts, symmetries, asymptotes, and graph of the

    y^2 = x (x - 1) (x - 2)


    i just have a very limited brain. need your guide and assistance guys. ( Sir ) God Bless

    thanks
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  2. #2
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    Re: possible flow of solution of the equation

    Quote Originally Posted by rcs View Post
    what is the domain, range, intercepts, symmetries, asymptotes, and graph of the

    y^2 = x (x - 1) (x - 2)


    i just have a very limited brain. need your guide and assistance guys. ( Sir ) God Bless

    thanks
    I hope this doesn't come too late ...

    1. Domain: Since y^2 \ge 0 the RHS of the equation must be greater or equal zero too.

    x (x - 1) (x - 2) \ge 0~\implies~ x \ge 0 If x < 0 then the other 2 factors are also negative which yields a negative result.

    You now have to examine under the condition that x \ge 0

    (x - 1) (x - 2) \ge 0~\implies~ \underbrace{x-1\ge 0 \wedge x-2 \ge 0}_{x\ge 2}~\vee~ \underbrace{x-1 \le 0 \wedge x-2 \le 0}_{0 \le x \le 1}

    2. Range: In general y \in \mathbb{R}. But since the domain is split into 2 seperated intervals you have to find (especially for the 1st interval) any existing maximum values. Use calculus.

    3. Intercepts:

    x-intercepts occur if y = 0. Since you have the term of y^2 in factored form the x-intercepts are easily to determine.

    y-intercepts occur if x = 0. So one x-intercept coincide with the y-intercept.

    4. Symmetries: What do you know about graphs whose one variable is squared?

    5. Asymptotes: a(x)=\lim_{x \to \infty} y

    You have to consider to different equations of y. (One asymptote is drawn in blue)
    Attached Thumbnails Attached Thumbnails possible flow of solution of the equation-relatgraph.png  
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