Thread: 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

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 the RHS of the equation must be greater or equal zero too.

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



2. Range: In general . 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:

You have to consider to different equations of y. (One asymptote is drawn in blue)