# MAT - Paper 2018 - Q2

> Source: https://ollybritton.com/notes/maths/problems/mat/2018/q2/ · Updated: 2021-10-27 · Tags: mat, notes, maths

## 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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