Lec1. Function

Question 1

What is a function?

Answer 1

a triple tuple / a subset of domain x codomaince

Question 2

Explain this: (U,V,G)

Answer 2

f(u,v) ∈ G
G is the subset of UxV
U is the domain/a set of all input variables
V is the codomain/a set of all input variables
G is a set of graph

Question 3

What is the requirement of a function

Answer 3

map elements from one set to another set such that for every x ∈ X, there is EXACTLY ONE y ∈ Y

Question 4

What is image and preimage in f(u) =v

Answer 4

u is the preimage of v under f
v is the image of u under f

Question 5

What is the domain of definition of f?

Answer 5

it must be a subset of U
u of U must has its image under f

Question 6

True/False: We have a function f maps x to y –> (x,y) ∈ f is the same as f(x) = y

Answer 6

True

Question 7

What is the range of f?

Answer 7

it must be subset of V (codomaince)
v of V must has its preimage under f

Question 8

What is another name for codomain?

Answer 8

Target

Question 9

True/False: f maps an element of the domain to 0 elements or to more than one target is WELL-DEFINED?

Answer 9

False

Question 10

What required for the 2 functions to be equal?

Answer 10

if they have the same domain and codomaince => f(x) = g(x)

Question 11

___ is a special type of function in which the domain is a set of consecutive integers

Answer 11

sequence

Question 12

Notation for a term of a sequence

Answer 12

gk instead of g(k)
- k in the index

Question 13

A sequence with a finite domain is called a _____ in which there is an initial index m and a final index n where n ≥ m

Answer 13

finite sequence

Question 14

A sequence with an infinite domain is called an ______ where there is an initial index m and the sequence is defined for all indices k such that k ≥ m

Answer 14

infinite sequence

Question 15

A sequence ____ showing how the value of ak depends on k. For ex: dk = 2^ k for k > 1
{dk} = 2, 4, 6,…

Answer 15

explicit formula