Page 25 - Algebra 1

Functions
When X and Y are two sets, a relation ‘f’ from set X or set Y is a function when every element of set X has a unique component in set Y.
or
A function from f is a relation when no two pairs have the same first element.
f: X → Y means that f is a function from X to Y, where X is the domain, and Y is the co-domain. For every element of x € X, there is a unique element y € Y.
Set X is the domain of the function.
Set Y is the co-domain of the function.
Set Z of all the numbers of Y assigned to members of X by the function is called the range of a function.
For example, the relation {(2, 3), (3, 4), (4,5), (5, 6)} is a function because no two ordered pairs have the same first component.
Domain = {2, 3, 4, 5}
Range = {3, 4, 5, 6}
When denoting range and function, we use different types of brackets based on the given function.
() – not including both the number is not included in the domain or the range. ∞ is not included so when representing ∞, always use ( or ).
[] – including, both the points are included. For example, if the range of the function is [0, 4], it includes all numbers between 0 and 4, with both numbers included.
{} – specific points, when the range or domain has a specific value.
f : X → Y is denoted by y = f(x)
For example, x > 2, f(x) = 2x + 1 and for -1 ≤ x ≤ 1, f(x) = x – 2 The value of f(3) + f(1) = (2(3) + 1) + (1 – 2) = 7 – 1 = 6
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ALGEBRA