What happens to a graph during a translation ?

During a translation , the graph is moved in the xy plane, but its shape , size , and orientation remain unchanged .

What happens to y -coordinates during a horizontal translation ?

During a horizontal translation , the y -coordinates are unchanged .

What happens to x -coordinates during a vertical translation ?

During a vertical translation , the x -coordinates are unchanged .

True or False? A reflection changes the size of the graph.

False. A reflection does not change the size of the graph, it only changes its position and orientation.

What happens to x -coordinates during a horizontal reflection ?

During a horizontal reflection, the x -coordinates change sign . E.g. A point (2, -6) becomes (-2, -6) during a horizontal reflection in the y -axis.

What happens to x -coordinates during a vertical reflection ?

During a vertical reflection, the x -coordinates stay the same . E.g. A point (2, -6) becomes (2, 6) during a vertical reflection in the x -axis.

What stays the same during a vertical reflection ?

During a vertical reflection , the x -coordinate of each point and any vertical asymptotes stay the same .

What happens to a graph when it undergoes a stretch ?

When a graph undergoes a stretch it is stretched about one of the coordinate axes by a scale factor . The size of the graph changes but its orientation stays the same .

Define scale factor .

A scale factor is a constant that determines how much a graph is stretched. E.g. a stretch by a scale factor of 2 means that the distance between each point on the graph and the relevant axis is multiplied by 2.

True or False? A stretch with a scale factor less than 1 is called a compression .

False. A stretch with a scale factor less than 1 is not called a compression . In exams, you must use the term " stretch " even for scale factors between 0 and 1.

What happens to the points on a graph undergoing a stretch when a scale factor is bigger than 1 ?

When a graph undergoes a stretch where the scale factor is bigger than 1 , the points on the graph get further away from the relevant axis.

What happens to y -coordinates during a horizontal stretch ?

During a horizontal stretch, the y -coordinates stay the same . E.g. A point (2, -5), undergoing a horizontal stretch with scale factor 3, becomes (6, -5).

What happens to y -coordinates during a vertical stretch ?

During a vertical stretch, each y -coordinate is multiplied by the scale factor . E.g. A point (2, -5), undergoing a vertical stretch with scale factor 3, becomes (2, -15).

True or False? Because horizontal and vertical transformations are dependent on each other, the order in which they are performed makes a difference.

False. Horizontal and vertical transformations are independent of each other. Because the transformations work in different directions, they do not affect each other so can be performed in any order .

True or False? When more than one transformation is applied to a function in the same direction , (i.e. two or more horizontal transformations or two or more vertical ones), the order in which the transformations are applied matters .

True. When more than one transformation is applied to a function in the same direction , the order in which the transformations are applied matters . E.g. if a horizontal stretch and a horizontal translation are applied to the same function, the final graph will be different depending on which transformation is applied first.

IBMathsDPAnalysis & Approaches (AA)SLFlashcards2. FunctionsTransformations of Graphs

Transformations of Graphs (DP IB Analysis & Approaches (AA))

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What happens to a graph during a translation?

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Cards in this collection (33)

What happens to a graph during a translation?
During a translation, the graph is moved in the xy plane, but its shape, size, and orientation remain unchanged.
What is a translation vector?
A translation vector describes how far a graph is moved.
The top value specifies how far left/right and the bottom value how far up/down.
E.g. the translation vector $(\begin{matrix} 3 \\ - 7 \end{matrix})$ describes a translation of 3 units in the positive x-direction and 7 units in the negative y-direction.
How is a horizontal translation represented in a function?
A horizontal translation is represented in a function by the notation $f (x + a)$ .
This describes a translation of the function $f (x)$ by $- a$ units in the x-direction.
Note that the sign inside the brackets is the opposite of the direction of movement.
What happens to x-coordinates during a horizontal translation?
During a horizontal translation, described by $f (x + a)$ , the x-coordinates are translated by $- a$ units in the x-direction.
What happens to y-coordinates during a horizontal translation?
During a horizontal translation, the y-coordinates are unchanged.
True or False?
Vertical asymptotes stay the same during a horizontal translation.
False.
Vertical asymptotes do not stay the same during a horizontal translation.
How is a vertical translation represented in a function?
A vertical translation is represented in a function by the notation $f (x) + a$ .
This describes a translation of the function $f (x)$ by $a$ units in the positive y-direction.
Note that the sign inside the brackets is the same as the direction of movement.
What happens to x-coordinates during a vertical translation?
During a vertical translation, the x-coordinates are unchanged.
What happens to y-coordinates during a vertical translation?
During a vertical translation, for a translation described by $f (x) + a$ , the y-coordinates are translated by $a$ units in the positive y-direction.
True or False?
Vertical asymptotes stay the same during a vertical translation.
True.
Vertical asymptotes stay the same during a vertical translation.
True or False?
A reflection changes the size of the graph.
False.
A reflection does not change the size of the graph, it only changes its position and orientation.
How is a horizontal reflection represented in a function?
A horizontal reflection is represented in a function by the notation $f (- x)$ .
This describes a reflection of the function $f (x)$ across the y-axis.
What happens to x-coordinates during a horizontal reflection?
During a horizontal reflection, the x-coordinates change sign.
E.g. A point (2, -6) becomes (-2, -6) during a horizontal reflection in the y-axis.
True or False?
Vertical asymptotes stay the same during a horizontal reflection.
False.
Vertical asymptotes do not stay the same during a horizontal reflection.
How is a vertical reflection represented in a function?
A vertical reflection is represented in a function by the notation $- f (x)$ .
This describes a translation of the function $f (x)$ across the x-axis.
What happens to x-coordinates during a vertical reflection?
During a vertical reflection, the x-coordinates stay the same.
E.g. A point (2, -6) becomes (2, 6) during a vertical reflection in the x-axis.
True or False?
The equation of a horizontal asymptote will change during a vertical reflection.
True.
The equation of a horizontal asymptote will change during a vertical reflection.
What stays the same during a vertical reflection?
During a vertical reflection, the x-coordinate of each point and any vertical asymptotes stay the same.
What happens to a graph when it undergoes a stretch?
When a graph undergoes a stretch it is stretched about one of the coordinate axes by a scale factor.
The size of the graph changes but its orientation stays the same.
Define scale factor.
A scale factor is a constant that determines how much a graph is stretched.
E.g. a stretch by a scale factor of 2 means that the distance between each point on the graph and the relevant axis is multiplied by 2.
True or False?
A stretch with a scale factor less than 1 is called a compression.
False.
A stretch with a scale factor less than 1 is not called a compression.
In exams, you must use the term "stretch" even for scale factors between 0 and 1.
What happens to the points on a graph undergoing a stretch when a scale factor is bigger than 1?
When a graph undergoes a stretch where the scale factor is bigger than 1, the points on the graph get further away from the relevant axis.
What is the equation for a horizontal stretch of a graph $f (x)$ by scale factor $q$ ?
The equation for a horizontal stretch of a graph $f (x)$ by scale factor $q$ is $f (\frac{1}{q} x)$
What is the equation for a vertical stretch of a graph $f (x)$ by scale factor $p$ ?
The equation for a vertical stretch of a graph $f (x)$ by scale factor $p$ is $p f (x)$
What happens to y-coordinates during a horizontal stretch?
During a horizontal stretch, the y-coordinates stay the same.
E.g. A point (2, -5), undergoing a horizontal stretch with scale factor 3, becomes (6, -5).
True or False?
Vertical asymptotes stay the same during a horizontal stretch.
False.
Vertical asymptotes do not stay the same during a horizontal stretch.
What happens to y-coordinates during a vertical stretch?
During a vertical stretch, each y-coordinate is multiplied by the scale factor.
E.g. A point (2, -5), undergoing a vertical stretch with scale factor 3, becomes (2, -15).
True or False?
For a horizontal stretch, the scale factor is the reciprocal of the coefficient of x.
True.
For a horizontal stretch, the scale factor is the reciprocal of the coefficient of x.
E.g. for a function $f (x)$ , the notation for a horizontal stretch of scale factor 2 is $f (\frac{1}{2} x)$ .
True or False?
Because horizontal and vertical transformations are dependent on each other, the order in which they are performed makes a difference.
False.
Horizontal and vertical transformations are independent of each other.
Because the transformations work in different directions, they do not affect each other so can be performed in any order.
True or False?
When more than one transformation is applied to a function in the same direction, (i.e. two or more horizontal transformations or two or more vertical ones), the order in which the transformations are applied matters.
True.
When more than one transformation is applied to a function in the same direction, the order in which the transformations are applied matters.
E.g. if a horizontal stretch and a horizontal translation are applied to the same function, the final graph will be different depending on which transformation is applied first.
What is the equation for a vertical stretch by factor $a$ followed by a translation $(0, b)$ ?
The equation for a vertical stretch by factor $a$ followed by a translation $(0, b)$ is $y = a f (x) + b$ .
What is the equation for a translation $(0, b)$ followed by a vertical stretch by factor $a$ ?
The equation for a translation $(0, b)$ followed by a vertical stretch by factor $a$ is $y = a [f (x) + b]$ .
True or False?
If a function undergoes multiple vertical transformations, the order of transformations is determined by the order of operations in the equation.
True.
If a function undergoes multiple vertical transformations, the order of transformations is determined by the order of operations in the equation.
E.g. for a function $2 (f (x) - 8)$ , the brackets comes before multiplication, so a translation of -8 is followed by a stretch of scale factor 2 (both in the y-direction).