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FUNCTİONS - Coggle Diagram
FUNCTİONS
Types of Functions
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One To One Functions
The image of each element in the domain is
different than one another;f : A--> B for any
a, b belongs to A
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Constant Function
Given f:A-->B if f maps all the elements of set A to one and only one element of set B, this function is
called a constant function and it is denoted by f(x)= c where c is a constant.
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Linear Functions
For any real numbers a and b,f :R--> R
f(x) = y ax+b is a linear function.
The graph of it is a line.
Equal Functions
Let f : A -->B and g: A--> B ,If
f(x) =g(x) then f and g are called equal functions
Identity Function
If A is a set. The function
I: A--> A defined by
I(x) --> x for all
x belonges to A is an identity function
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Piecewise Functions
Sometimes a function can’t be described by a single equation, and instead we have to describe it using a combination of equations.
Note: In the piecewise function, the rule of the function changes for the disjoint subsets of the
domain.
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Inverse Of A Function
For
x belongs to A; if whenever f(x)=y,f-1(y)=x.Then the function of f-1 is said to be the inverse of function f.
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When f : A--> B and the function y = f(x) is given,
it is supposed to be 1-1 and onto.İf not then its inverse would not be a function.
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Graphs Of Functions
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Vertical Line Test
To determine whether a graph represents a function, vertical lines can be drawn on the graph.If the lines intersect with more than one point on x axis,it is not a function.If they dont,it is a function
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What is a function?
A function is a correspondence, or rule, that pairs each element of a set(the domain)with
exactly one element of another set(the codomain)
İf there is an output to each input and a unique output to each input,the relationship that is satisfied by two variables is called a function
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