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FUNCTIONS, f(x) = 3x, Slayt9-Fonksiyonun_Tanim_KUmesi_ile_Deger_KUmesinin…
FUNCTIONS
A function is a correspondence,or rule, that pairs each element of a set(the domain) with exactly one element of another set (the range)
Types of Functions
Unit function
f:R -> R; f(x)= x
f: z -> z; f(x)=x
Constant function
is a constant function is a function who output value is the same for every input value.
f(x)= 7, f(10)= 7, f(1)= 7, f(200)= 7
Examples:
Linear function
the function f(x)= mx+n is linear function.
f(x)= 2x-3 , f(x)= 10
is equal to first degree equations
Identity function
f(1)= 1 , f(2)=2 , f(10)=10 , f(2x+1)= 2x+1
Equality of Two Functions
If f(x) = g(x) for all elements of A, then the function f and g are called equal functions and denoted by f=g .
One-to-One Function
Each element of one set, for example Set (A) is mapped with a unique element of another set, say, Set (B).
f(x) = x + 1
Example
Into & Onto Functions
Into
is a type of function where at least one element of the co-domain will not have a pre-image in the domain.
example:
C = {a, b, c}, D = {1, 2, 3, 4} ; f = {(a, 1), (b, 2), (c, 3)}
Onto
If A and B are the two sets, if for every element of B, there is at least one or more element matching with set A, it is called onto function.
example:
C = {1, 2, 3, 4} , D = {x, q, s} and f = {(1, q) , (2, x) , (3, s) , (4, s)}
Function notation
examples
f(x) = 2x+1
f(x) = 5x-1
Any letter can be used for notation.
Ex:
g(x), h(x), p(x), etc.
Domain
A= {2,4,9,11}
B= {6,12,14,21,33,79,36}
Range
Image
f(A)= {6,12,36,33}
f(x) = 3x
