Algebraic Functions
Theses are functions that are con
structed my adding, subtracting, multiplying or taking roots
of polynomials.
Ex. 1.
Find the domain of
f
(
x
) =
√
x
. Draw the graph.
1
2
Ex.
2.
Find the domain of
f
(
x
) =
√
x
2
+ 1
.
Draw the
graph.
3
Ex.
3.
Find the domain of
f
(
x
) =
√
x
2

1
.
Draw the
graph.
4
Ex. 4.
Find the domain of
f
(
x
) =
4
√
(
x

3)(
x
+2)
x

1
.
5
Summary
6
Trigonometric Function
Trigonometry means the study of angles inside a triangles.
There are two (equivalent) ways of thinking abut trigono
metric functions. By looking at angles inside a triangle, or
by looking at a unit circle.
Two ways of measuring angles: radian vs degree
Unit Circle
7
f
(
t
) = sin(
t
)
f
(
t
) = cos(
t
)
8
For any periodic function:
•
the
Amplitude
is half the distance between the max
imum and minimum values.
•
Period
is th smallest time needed for the function to
execute one complete cycle.
To describe an arbitrary amplitude and period of a sinu
soidal functions, we use functions of the form
f
(
t
) =
A
sin(
Bt
)
g
(
t
) =
A
cos(
Bt
)
where

A

is the amplitude and 2
π/

B

is the period.
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 Fall '19
 Trigonometry, Exponential Function, Derivative, Exponential decay