MAT106: Trigonometry
Function Transformations Determining Functions
1.
Write a single function ( ) that results from transforming the parent
function ( )
as follows: a horizontal translation
units left,
then a vertical translation
units down.
2.
Write a s
MAT106: Trigonometry
Arithmetic Facts Involving Cube Roots, Fourth Roots, and Related Items
Powers to Know:
Additional Powers of
:
Rule for Simplifying Radicals with Radicands Involving Powers of Variables:
To simplify , divide the exponent of the radican
MAT106: Trigonometry
Justifications/Proofs of Various Properties of Logarithms
Below are basic algebraic proofs of the validity of some of the basic properties of logarithms. In order
to proceed, the following basic facts should be noted:
a.
is equivalent
MAT106: Trigonometry
Brief Summary of Function Transformations
The sections below are intended to provide a brief overview and summary of the various types of basic
function transformations covered in this course. Detailed explanations are not included, b
MAT106: Trigonometry
Function Transformations Analyzing Functions
Basic Function:
()
1. a. Graph ( )
.
b. State the type of graph.
2
a. Graph ( )
.
b. Analyze the change from #1 above.
).
3. a. Graph ( ) (
b. Analyze the change from #1 above.
()
()
4. a.
MAT106: Trigonometry
Quiz on Sections 2.1-2.3, Version A: Function Transformations and Symmetry Solutions
(
1.
2.
)
(
)
)
(
)
(
)
(
)
()
()
Translated
units left
Compressed horizontally by a factor of
Reflected over the x-axis
()
4.
(
()
(
3.
)
(
Add
to
M
MAT106: Trigonometry
Quiz on Sections 2.1-2.3, Version B: Function Transformations and Symmetry Solutions
(
1.
2.
]
(
)
Apply horizontal transformations, in order, to given domain:
1) Translate
unit right: Add
[
]
[
to each x-value
]
2) Stretch horizontal
MAT106: Trigonometry
Quiz on Sections 2.1-2.3, Version D: Function Transformations and Symmetry Solutions
(
1.
2.
]
Apply vertical transformations, in order, to given range:
1) Stretch vertically by a factor of
[
2) Translate
[
Final answer:
]
[
]
units u