This document discusses different types of transformations of graphs: dilations, reflections, and translations. Dilations make graphs steeper or flatter by stretching or compressing along an axis. Reflections flip graphs across an axis, acting as a mirror. Translations shift graphs sideways, up, or down without changing their shape. The order for performing multiple transformations is DRT (Dilation, Reflection, Translation).

1. Maths Methods
Transformations of graphs
K McMullen 2012

2. Transformations
Transformations help us explain how an original
basic function has been transformed to create a
new function
Transformations include Dilations, Reflections,
and Translations
Always do your transformations in this order-
remember D-R-T (DiRT, although there’s no i)
K McMullen 2012

3. Transformations
Dilation: makes the graph steeper or flatter
Dilation from the x-axis (parallel to the y-axis):
Stretches or compresses (dependent on the
dilation factor) along the y-axis
Dilation from the y-axis (parallel to the x-axis):
stretches or compresses (dependent on the
dilation factor) along the x-axis
K McMullen 2012

4. Transformations
Reflection: reflects the graph along the axis
(does not changes the shape of the graph)
Reflection in the x-axis: A reflection in the x-axis
changes the sign of the y-coordinates while
leaving the x-coordinates unchanged. The x-axis
acts as a mirror.
Reflection in the y-axis: A reflection in the y-axis
changes the sign of the x-coordinates while
leaving the y-coordinates unchanged. The y-axis
acts as a mirror.
K McMullen 2012

5. Transformations
Translation: shifts the entire graph sideways or
up or down (does not change the shape of the
graph)
Horizontal translation (parallel to the x-axis): it
slides the graph to the left or right
Vertical translation (parallel to the y-axis): it slides
the graph up or down
K McMullen 2012

6. Translations
Table on pg.33 of notes
Also, refer to page 120 of textbook for another
table summarising the features of different graphs
Answer the following questions:
2A: 1-9
2B: 1-12
2C: 1-11
2D: 1-12
2E: 1-12
K McMullen 2012