# Thread: possible flow of solution of the equation

1. ## 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

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

Originally Posted by rcs
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)