# Maths - Transformations

What is the transformation as a vector for $y = f(x) + a$?

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 $y = f(x + a)$?

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 $a$?

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

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

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.

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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 $f(2x)$?

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.