are
called hyperbolae. One is illustrated below.
A Level Maths Notes: C1 – Transformations of Graphs
The graphs given by the equationare
called hyperbolae. One is illustrated below.
In fact there are a set of equations which all give the same shape
of graph as shown above. The graphs may be moved up or down,
translated, rotated or any combination of these, but the shapes of
the graphs are still fundamentally the same. The rules of
transformation are just the normal transformation of graph rules. For
simple transformations like these, it does not matter whether you
apply
or
–
transformations first.
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Example: Sketch the graph
There are two transformations: a translation 3 in the–
direction and a scaling by 2 in the–
direction. The graph is sketched below.
Translate
the graph left 3.
Translate
the graph up 2.
Scale
the graph by a factor 3 in the
Scale
the graph by a factor 2 in the
Reflect
the graph in the
Reflect
the graph in the