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Various graph transformations including horizontal and vertical shifts, compressions and stretches, and reflections about the x-axis or y-axis. It provides examples of different types of shifts and compressions, and demonstrates how to apply multiple transformations to a base function.
Typology: Lecture notes
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Transformations are when we make changes to the base functions from Section
3.4 to graph more complicated functions.
Methods
Order of Transformations
Vertical Translations vs. Horizontal Translations
Vertical
Up
ଶ
Down
ଶ
Horizontal
ଶ
Right
ଶ
Ex. What kind of shifts are these?
ଷ
Vertical
య
Compression
ଵ
௩
య
Horizontal
௫
3
3
For the following graphs, provide (a) the base function, (b) which transformations
were performed, (c) the equation of the function. Hint: There are not vertical or
horizontal stretched or compressions.
(c)
య
(c) −
ට
3
ට
3
(c)