# Maths - Transformations

> Source: https://ollybritton.com/notes/a-level/maths/topics/transformations/ · Updated: 2021-01-06 · Tags: maths, school, year-1

##### What is the transformation as a vector for $y = f(x) + a$??
$$
\left(\begin{matrix} 0 \\\\ a \end{matrix}\right)
$$

##### What does the transformation $y = f(x) + a$ mean in simple terms??
Move the graph up by $a$.

##### What is the transformation as a vector for $y = f(x + a)$??
$$
\left(\begin{matrix} -a \\\\ 0 \end{matrix}\right)
$$

##### What does the transformation $y = f(x + a)$ mean in simple terms??
Move the graph back horizontally by $a$.

##### What is the transformation to $f(x)$ to make the graph forwards by $a$??
$$
f(x - a)
$$

##### What is the transformation to $f(x)$ to move the graph down by $c$??
$$
f(x) - c
$$

##### What is the equation of line for the asymptote of $\frac{1}{x}$ at $y = 0$ when you transform it by doing $\frac{1}{x} + 1$??
$$
y = 1
$$

##### What does the transformation $y = af(x)$ mean??
A vertical stretch by scale factor $a$.

##### What does the transformation $y = f(ax)$ meant??
A horizontal stretch by scale factor $\frac{1}{a}$.

##### If a quadratic has roots $(3, 0)$ and $(-3, 0)$ and undergoes the transformation $y = f(2x)$, what are the new roots??
$(1.5,0)$ and $(-1.5,0)$

##### What's another way of saying a horizontal stretch by scale factor $\frac{1}{2}$??
The $x$-coordinates halve.

##### What is the transformation for $y = -f(x)$??
A reflection in the $x$-axis.

##### What is the transformation for $y = f(-x)$??
A reflection in the $y$-axis.

##### What do transformations "outside" the function represent??
Vertical transformations.

##### What do transformations "inside" the function represent??
Horizontal transformations.

### 2021-01-07
##### What happens to the co-ordinates for $f(2x)$??
They all halve.

##### If the original point for $f(x)$ is $(4, 14)$, what is the new co-ordinate for $f(2x)$??
$$
(2, 14)
$$

##### Which points stay in place for a transformation like $f(ax)$??
The points on the $y$-axis.

##### Which points stay in place for a transformation like $af(x)$??
The roots, i.e. the points on the $x$-axis.

##### When given a transformation question where you're asked to sketch a graph, what should you do first??
Describe the transformation in plain English.

##### What happens to the co-ordinate $(2,4)$ for $2f(x)$??
$$
(2, 8)
$$

##### What happens to the co-ordinate $(3,6)$ for $f\left(\frac{1}{2}x\right)$??
$$
(6, 6)
$$

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