Functions

Question 1

Define functions

Answer 1

a function from a non-empty set A to a non-empty set B is an assignment of each element of A to exactly one element of B

A function is denoted by A –> B

We write f (a) = b if b is the unique element of B assigned by the function f to the element a of A. A clear defined output of one element.

Question 2

Define function equality

Answer 2

Two functions are equal they have the same domain, the same codomain and map each element of the domain the same element of the codomain

Question 3

What is a sequence

Answer 3

a sequence is a function from a subset of the integer

Question 4

What is a geometric progression

Answer 4

a geometric progression is a sequence of the form: a, ar, ar 2 … where the initial term a and the common ratio r are real numbers

Question 5

What is an arithmetic progression

Answer 5

an arithmetic progression is a sequence of the form a, a + d, a+ 2d, a+3d where the initial term a and the common difference d are real numbers

Question 6

Define a recurrence relation

Answer 6

a recurrance relation for the sequence a n is an equation that expresses an in terms of one or more of the previous terms of the sequence

Question 7

How do you solve a recurrence relation

Answer 7

finding the formula for the nth term of the sequence generated by a recurrence relation is called solving the recurrence relation, such a formula is called a closed formula

Question 8

What does injective mean

Answer 8

one to one, each value in the range of corresponds to exactly one element in the domain, codomain cant have many domain

Question 9

What does surjective (onto) mean

Answer 9

every element in the codomain maps to at least one element in the domain

Question 10

What does bijective mean

Answer 10

only one mapping from each element and no value of the codomain is alone. It is both injective and bijective