What is a translation ?

A translation is a change that moves the whole graph in the x and/or y direction .

In the equation of a graph, what kind of mathematical function indicates a vertical translation ?

The addition or subtraction of a constant to an equation of a graph indicates a vertical translation .

What does it mean to describe a translation fully ?

To describe a translation fully, you must include: the transformation (translation) and the vector or worded description of the translation

What is the relationship between a reflection and a stretch of a graph?

A reflection is a special case of a stretch where the stretch scale factor is -1 .

What are invariant points ?

Invariant points are points on a graph that do not change during a particular transformation.

IGCSEMaths A: HigherEdexcelFlashcards

Transformations of Graphs (Edexcel IGCSE Maths A)

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FrontTranslations of Graphs
What is a translation?

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What is a translation?
A translation is a change that moves the whole graph in the x and/or y direction.
Define translation in terms of vectors.
A translation can be described as a vector $(\begin{matrix} x \\ y \end{matrix})$ where $x$ is the movement in the $x$ -direction and $y$ is the movement in the $y$ -direction.
In the equation of a graph, what kind of mathematical function indicates a vertical translation?
The addition or subtraction of a constant to an equation of a graph indicates a vertical translation.
What type of translation is represented by the notation $y = f (x + a)$ ?
$y = f (x + a)$ represents a translation of $- a$ units in the $x$ -direction (which is $a$ units to the left).
What type of translation is represented by the notation $y = f (x) + b$ ?
$y = f (x) + b$ represents a translation of $+ b$ units in the $y$ -direction (this is $b$ units up).
True or False?
$y = f (x - 3) + 2$ means a translation of $- 3$ in the $x$ -direction and $+ 2$ in the $y$ -direction.
False.
$y = f (x - 3) + 2$ means a translation of $+ 3$ in the $x$ -direction and $+ 2$ in the $y$ -direction.
What does it mean to describe a translation fully?
To describe a translation fully, you must include:
- the transformation (translation)
- and the vector or worded description of the translation
What is the equation for a translation of 5 units to the left and 3 units up?
$y = f (x + 5) + 3$ is the equation for a translation of $5$ units to the left and $3$ units up.
True or False?
If a constant is added to the overall function, this indicates a translation in the $x$ -direction.
False.
If a constant is added to the overall function, this indicates a translation in the $y$ -direction.
True or False?
Key points that are labelled with coordinates on a graph should be translated by the same vector as the graph.
True.
Key points that are labelled with coordinates on a graph should be translated by the same vector as the graph.
For example, If a point $P (2, 7)$ lies on the graph $y = f (x)$ , which is transformed to the graph $y = f (x + 3)$ , then the point $P$ will also undergo a translation of $- 3$ units in the $x$ -direction, giving it new coordinates of $(- 1, 7)$ .
What is the equation for a reflection in the $x$ -axis of $y = f (x)$ ?
The equation for a reflection in the $x$ -axis of $y = f (x)$ is $y = - f (x)$ .
What is the equation for a reflection in the $y$ -axis of $y = f (x)$ ?
The equation for a reflection in the $y$ -axis of $y = f (x)$ is $y = f (- x)$ .
What is the relationship between a reflection and a stretch of a graph?
A reflection is a special case of a stretch where the stretch scale factor is -1.
True or False?
$y = - f (- x)$ represents a reflection in both the $x$ -axis and $y$ -axis.
True.
$y = - f (- x)$ represents a reflection in both the $x$ -axis and $y$ -axis.
True or False?
The equation $y = - f (x)$ reverses the sign of all of the $x$ -coordinates in the function $y = f (x)$ .
False.
The equation $y = - f (x)$ reverses the sign of all of the $y$ -coordinates in the function $y = f (x)$ , reflecting the graph up/down across the $x$ -axis.
True or False?
The equation $y = f (- x)$ reverses the sign of all the $x$ -coordinates in the function $y = f (x)$ .
True.
$y = f (- x)$ reverses the sign of all the $x$ -coordinates of the function $y = f (x)$ , reflecting the graph left/right across the $y$ -axis.
What is a stretch in the context of transformations of graphs?
In the context of transformations of graphs, a stretch is a transformation that enlarges or shrinks the graph in the $x$ -direction or $y$ -direction.
What transformation of the graph of $y = f (x)$ is indicated by the equation $y = f (a x) ?$
$y = f (a x)$ is a horizontal stretch (stretch in the $x$ -direction) by a scale factor of $\frac{1}{a}$ .
What transformation of the graph of $y = f (x)$ is indicated by the equation $y = a f (x) ?$
$y = a f (x)$ is a vertical stretch (stretch in the $y$ -direction) by a scale factor of $a$ .
True or False?
The equation $y = f (2 x)$ represents a horizontal stretch by a factor of $2$ .
False.
$y = f (2 x)$ represents a horizontal stretch by a factor of $\frac{1}{2}$ .
Remember that the scale factor of a stretch in the $x$ -direction is the reciprocal of the coefficient of $x$ .
What are invariant points?
Invariant points are points on a graph that do not change during a particular transformation.
What is the equation for a horizontal stretch of $y = f (x)$ by a factor of $\frac{1}{3}$ ?
The equation for a horizontal stretch of $y = f (x)$ by a factor of $\frac{1}{3}$ is $y = f (3 x)$ .
True or False?
$y = 3 f (x)$ represents a vertical stretch by a factor of 3.
True.
$y = 3 f (x)$ represents a vertical stretch by a factor of 3.
What is the equation for a vertical stretch of $y = f (x)$ by a factor of $4$ ?
The equation for a vertical stretch of $y = f (x)$ by a factor of $4$ is $y = 4 f (x)$ .
True or False?
Points on the $y$ -axis are invariant during a vertical stretch.
False.
Points on the $x$ -axis are invariant during a vertical stretch.

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2. Equations, Formulae & Identities

3. Sequences, Functions & Graphs

4. Geometry & Trigonometry

5. Vectors & Transformation Geometry

6. Statistics & Probability