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 where
is the movement in the
-direction and
is the movement in the
-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 ?
represents a translation of
units in the
-direction (which is
units to the left).
What type of translation is represented by the notation ?
represents a translation of
units in the
-direction (this is
units up).
True or False?
means a translation of
in the
-direction and
in the
-direction.
False.
means a translation of
in the
-direction and
in the
-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?
is the equation for a translation of
units to the left and
units up.
True or False?
If a constant is added to the overall function, this indicates a translation in the -direction.
False.
If a constant is added to the overall function, this indicates a translation in the -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 lies on the graph
, which is transformed to the graph
, then the point
will also undergo a translation of
units in the
-direction, giving it new coordinates of
.
What is the equation for a reflection in the -axis of
?
The equation for a reflection in the -axis of
is
.
What is the equation for a reflection in the -axis of
?
The equation for a reflection in the -axis of
is
.
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?
represents a reflection in both the
-axis and
-axis.
True.
represents a reflection in both the
-axis and
-axis.
True or False?
The equation reverses the sign of all of the
-coordinates in the function
.
False.
The equation reverses the sign of all of the
-coordinates in the function
, reflecting the graph up/down across the
-axis.
True or False?
The equation reverses the sign of all the
-coordinates in the function
.
True.
reverses the sign of all the
-coordinates of the function
, reflecting the graph left/right across the
-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 -direction or
-direction.
What transformation of the graph of is indicated by the equation
is a horizontal stretch (stretch in the
-direction) by a scale factor of
.
What transformation of the graph of is indicated by the equation
is a vertical stretch (stretch in the
-direction) by a scale factor of
.
True or False?
The equation represents a horizontal stretch by a factor of
.
False.
represents a horizontal stretch by a factor of
.
Remember that the scale factor of a stretch in the -direction is the reciprocal of the coefficient of
.
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 by a factor of
?
The equation for a horizontal stretch of by a factor of
is
.
True or False?
represents a vertical stretch by a factor of 3.
True.
represents a vertical stretch by a factor of 3.
What is the equation for a vertical stretch of by a factor of
?
The equation for a vertical stretch of by a factor of
is
.
True or False?
Points on the -axis are invariant during a vertical stretch.
False.
Points on the -axis are invariant during a vertical stretch.