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.
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 $f(2x)$?
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.