How are the graphs of y=x^2-3x and y=3x-x^2 related? I know that 3x-x^2 is a reflection of y=x^2-3x but what else do they have income besides that and their intersection points?

Same with the graphs of y=f(x) and x=f(y), how are they related?

Thank you.

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Originally Posted by phoenirius

How are the graphs of y=x^2-3x and y=3x-x^2 related? I know that 3x-x^2 is a reflection of y=x^2-3x but what else do they have income besides that and their intersection points?

Same with the graphs of y=f(x) and x=f(y), how are they related?

Thank you.

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multiple one equation by negative one to get the other.
(we multiple on both sides by negative to prove it)
y=3x-x^2
(-1)y=(-1)(3x-x^2)
(-1)y=(-1)(3x)-(-1)(x^2)
(-1)y=-3x +x^2
(-1)y=x^2-3x.

what do we know about equations that the slope of one times the slope of the other equals negative one? Does this relate to your question? Is this why they are a refleciton? What happens when a function is the opposite of another function by order? f(g(x)) versus the g(f(x))?
which variable is independent and which is dependent?
which one do you choose, and which one is determined by your choice? y= mx+b (slope intercept form has an x independent variable, and y depends on what x you choose, tradictionally).

I am not sure what else you want in the way of information or where your teacher or you are trying to go with the question.