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).
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
