Flashcards
2021-10-27
$$P(x, y) = (x + 1, y - 1)$$ $$Q(x, y) = (2x, 3y)$$ When working with composite functions that depend on two variables, how can you write out the intermediate step for $PQ(x, y)$??
$$ P(2x, 3y) $$
If you have a transformation $S$ that maps all points $$(x, y) \to (x + 1, y)$$ why is substituting $x = x + 1$ to find out the new equation of $$y = x^2 + 2x + 2$$ clearly not valid??
Because that’s a translation in the wrong direction.
What is the general co-ordinate for the quadratic $$y = x^2 + 2x + 2$$??
$$ (x, x^2 + 2x + 2) $$
What is the general co-ordinate for the quadratic $$y = x^2 + 2x + 2$$ after the transformation that maps $$(x, y) \to (x + 1, y)$$??
$$ (x + 1, x^2 + 2x + 2) $$
How could you could you work out a new equation for a curve that has been transformed to $$(x + 1, x^2 + 2x + 2)$$??
Make the substitutions
$$ u = x+1 $$
$$ v = x^2 + 2x + 2 $$
And then use the fact $x = u - 1$ to write a definition for $v$ in terms of $u$.
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date: 2021-10-27 17:01
summary: what is special about these two transformations of the xy-plane?
tags:
- '@?public'
- '@?mat'
- '@?notes'
- '@?maths'
title: MAT - Paper 2018 - Q2