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

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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 ( x๎€2๎€ + x + 3, etc.)
d. Exponential Functions
e. Logarithmic Functions (ln, log, etc.)
f. x๎€a
II. Power Functions ctn.
f(x) = x๎€a
a. a=n, n is a positive integer (ex: f(x) = x, f(x) = x๎€2๎€, f(x)= x๎€3๎€)
b. a= , n is positive (ex: f(x) = , f(x)=
n
1โˆšxโˆš
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) = b๎€x
b. F๎€-1๎€ (x) = log๎€b๎€x
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. Domain๎€: D
c. Range๎€: 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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Document Summary

Types of functions: there are five basic types of functions, trigonometric functions (sinx, cosx, etc. , polynomial functions ( x 2 + x + 3, etc. , exponential functions, logarithmic functions (ln, log, etc. ) f. x a. Power functions ctn. f(x) = x a: a=n, n is a positive integer (ex: f(x) = x, f(x) = x 2 , f(x)= x 3 , a, a= -n (ex: f(x)= Q(x) a: both the numerator and denominator are polynomials x+1, example of a rational function: x+5. Line test to determine if a graph is a function. It is a function if the vertical line only passes through the graph once. Even and odd functions: even: f(-x) = f(x), any x inside the domain https://www. sparknotes. com/math/algebra2/specialgraphs/section4, odd: f(-x) = -f(x) http://jwilson. coe. uga. edu/emt668/emat6680. f99/challen/iu/day7. html. Input: x g(x) f(g(x)) output x +12. Ex 1: f(x) = f(x) = f(x) = x x +12 f(-x) = -f (x) so the function is odd.

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