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Functions - Coggle Diagram
Functions
Identity Function
Identity function is a function that always returns the value that was used as its argument, unchanged. That is, when f is the identity function, the equality f(X) = X is true for all values of X to which f can be applied.
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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 as a constant function and is denoted by f(x) = c where c is a constant real number.
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Linear Function
The function f(x) = mx + n is called linear function where m,n ∈ R and m ≠ 0
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One-to-One Function
One to one function basically denotes the mapping of two sets. A function g is one-to-one if every element of the range of g corresponds to exactly one element of the domain of g.
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Into Function
If f: A→ B is such that there exists at least one element in codomain which is not the image of any element in domain, then f(x) is into.
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Onto Function
Let f be a function of A into B that is f : A → B. If f(A) = B, then f is called an onto function.
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Even Function
A function f is even if the following equation holds for all x and −x in the domain of f : f(x)=f(−x) f ( x ) = f ( − x ) Geometrically, the graph of an even function is symmetric with respect to the y -axis, meaning that its graph remains unchanged after reflection about the y -axis.
Odd Function
A function f is odd if the following equation holds for all x and −x in the domain of f : −f(x)=f(−x) − f ( x ) = f ( − x ) Geometrically, the graph of an odd function has rotational symmetry with respect to the origin, meaning that its graph remains unchanged after a rotation of 180∘ about the origin.
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