Sets Theory

A set is a collection of distinct objects, considered as an object in its own right. For example, the numbers 1, 3, and 5 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {1, 3, 5}. The concept of a set is one

Hyperbolic Functions: Definition, Inverse, Identities, Derivatives, & Examples

What is Hyperbolic functions? Hyperbolic function identic with trigonometry function especially sine and cosines. It is exponential functions that has properties like trigonometry. The basic of hyperbolic functions are hyperbolic sine and cosines. But the both of them are different with sine and cosines in trigonometry. In real life, it can be applied to determine

Set-Builder Notation

A Set is a collection of things (often numbers). Example: {2, 3, 5} is a set. Here is a simple example of set-builder notation: General Form: {formula for elements: restrictions} or {formula for elements| restrictions} Show the Type of Number You can show what type of number x is. Number Types Symbols Details N Natural Numbers

Intervals

Definition In mathematics, interval is a set of real numbers with the property that any number that lies between 2 numbers in the set is also included in the set. For example, the set of all numbers x satisfying 3 ≤ x ≤ 5 is an interval which contains 3, 5, and all numbers between them. Interval: all

Injective, Surjective & Bijective

Definition of Function Injective A function f is injective if and only if whenever f(x) = f(y), x = y. Surjective f is surjective if and only if f(A) = B A function f (from set A to B) is surjective if and only if for every y in B, there is at least one x in A such that f(x) = y Bijective

Set Symbols

Set Symbols – A Set is a collection of things, usually numbers. We can list each element or member of a set inside curly brackets like this: {2, 4, 6, 8, … } Three dots means goes on forever (infinite) Common Symbols Used in Set Theory Symbols save time and space when writing. Here are

Inverse Functions

Definition The inverse is shown by putting a little “-1” after the function name, like this: f-1(y), where y = f(x) It says “f inverse of y“ Here we have the function f(x) = 3x+2 The flow is Inverse Functions make 3x + 2 back to x , substitute y = 3x + 2, then So,

Function Transformations

How move and resize the graphs of functions? How move the graphs of functions? Add a constant to the y-value will move it up or down Add a constant to the x-value will move it left or right Examples Function c > 0 c < 0 f(x) = x2 g(x) = x2 + c        f(x)