Question

Is the only way to solve these kinds of questions to graph it and see visually? (Grade 11 beginner)

Answer 1

For exp. graph y = x^2, y=(2x)^2 , y = (1/2x)^2 find invariant points

Answer 2

would I have to graph those to find the invariant points?

Answer 3

do you know the definition of an invariant point?

Answer 4

How are "invariant points" defined?

Answer 5

Points that are the same?

Answer 6

the same as what? Look it up.

Answer 7

So basically you have y = (kx)^2 for k = (some range of numbers) and you want to find the values of x which always yield the same values of y, regardless of the values of k? If yes, the only point is (0,0) for this graph. (see attached).

Answer 8

made with: Geogebra --> http://www.geogebra.org

Answer 9

a fixed point = invariant point