# MAT - Paper 2018 - Q2

## 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 $u$.