True or False?
Translating a graph maintains its shape, size, and orientation.
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True or False?
Translating a graph maintains its shape, size, and orientation.
True.
Translating a graph maintains its shape, size, and orientation.
It only moves the graph up/down/left/right.
When a graph is translated by the vector , how many units does it move and in which direction(s)?
When a graph is translated by the vector , it moves units right and units upwards.
If is negative then it moves left, and if is negative it moves downwards.
A graph is transformed from to . Describe the transformation fully.
If a graph is transformed from to , this is a translation of units right.
A graph is transformed from to . Describe the transformation fully.
If a graph is transformed from to , it has been translated vertically upwards by units.
True or False?
When a graph is translated, any asymptotes remain in the same location(s).
False.
When a graph is translated, any asymptotes are also translated in the same way as the rest of the graph.
Outline how would you find a new equation for a graph which has been translated horizontally.
To find a new equation for a graph which has been translated horizontally, consider how the function has been changed.
It has changed from to , this is a translation of units right.
Therefore in the equation of the graph, you can simply replace with .
E.g. becomes .
Outline how would you find a new equation for a graph which has been translated vertically.
To find a new equation for a graph which has been translated vertically, consider how the function has been changed.
It has changed from to , this is a translation of units upwards.
Therefore in the equation of the graph, you can simply add on
E.g. becomes .
Describe the transformation that has occurred when is transformed to .
When is transformed to , it has been translated units right, and units upwards.
This is why when completing the square, the vertex is at .
The graph of is transformed to .
Describe the transformation that has occurred.
When the graph of is transformed to , the graph has been reflected in the x-axis.
The graph of is transformed to .
Describe the transformation that has occurred.
When the graph of is transformed to , the graph has been reflected in the y-axis.
True or False?
Some graphs appear not to change when reflected.
True.
Some graphs appear not to change when reflected.
E.g. will look exactly the same when reflected in the y-axis.
Outline how would you find a new equation for a graph which has been reflected in the x-axis.
To find a new equation for a graph which has been reflected in the x-axis, consider how the function has been changed.
It has changed from to .
Therefore you multiply the whole equation of the graph by -1.
E.g. becomes or .
Outline how would you find a new equation for a graph which has been reflected in the y-axis.
To find a new equation for a graph which has been reflected in the y-axis, consider how the function has been changed.
It has changed from to .
Therefore you replace all the 's with .
E.g. becomes or .
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.