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Lecture 3

MATH 2A Lecture Notes - Lecture 3: Inverse Function, Trigonometric FunctionsPremium


Department
Mathematics
Course Code
MATH 2A
Professor
Liu, W
Lecture
3

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Math 2A Lecture 3 - Functions ctn.
I. Types of Functions
a. There are five basic types of functions
b. Trigonometric Functions (sinx, cosx, etc.)
c. Polynomial Functions ( x2 + x + 3, etc.)
d. Exponential Functions
e. Logarithmic Functions (ln, log, etc.)
f. xa
II. Power Functions ctn.
f(x) = xa
a. a=n, n is a positive integer (ex: f(x) = x, f(x) = x2, f(x)= x3)
b. a= , n is positive (ex: f(x) = , f(x)=
n
1x
3x
c. a= -n (ex: f(x)= )
x
1
III. Rational Functions
a. f(x) = P(x)
Q(x)
b. Both the numerator and denominator are polynomials
c. Example of a rational function: x+5
x+1
IV. Logarithmic Functions
a. f(x) = bx
b. F-1 (x) = logbx
V. More Basics of Functions
a. Function(f): a rule that assigns to each element x in a set D with
exactly one element (f(x)).
b. Domain: D
c. Range: set of all possible values
d. For any input there is only one output. We can use the Vertical
Line Test to determine if a graph is a function. It is a function if the
vertical line only passes through the graph once.
Picture: https://en.wikipedia.org/wiki/Vertical_line_test
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