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FUNCTIONS - Coggle Diagram
FUNCTIONS
GRAPHS OF FUNCTIONS
Graphs Of Piecewise Functions: It is a function in which more than one formula is used to define the output.
Vertical Line Test: A graph represents a function if it is possible to draw a vertical line that intersects the graph more than once.
Graphs Of Linear Functions: If f is a linear function, then its graph is a line.
Piecewise Functions: We describe piecewise functions with combination of equations.
Odd Functions: If powers of x are only odd, then function is called odd function.
Domain: The domain of a function is the complete set of possible values of the independent variable.
Range: The range of a function is the complete set of all possible resulting values of the dependent variable, after we have substituted the domain.
Codomain: The codomain of a function is the set of its possible outputs.
IMPORTANT
Every element in the domain is related with an element in the range.
Any element in the domain must be related to only one element in the range.
Into Functions: Function f from set A to set B is into function. If at least set B has a element which is not connected with any of the element of set A.
Onto Functions: Function f from set A to set B is onto function if each element of set B is connected with set of A elements.
One To One Functions: If each elements of set A is connected with different elements of set B, then we call this function as one to one function.
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Equal Functions: Two functions are equal if they have the same domain and codomain and their values are the same for all elements of the domain.
Identity Functions: The domain and range elements are exactly the same.
Constant Functions: Given f : A to 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.
Linear Functions: For any real numbers a and b. F: R to R, f(x) = y = ax+b is said to be linear function.
Even Functions: If powers of x are only even, then function is called even function.
Neither Even Nor Odd: If the function has both even and odd powers of x then it is neither of them.
Composition of Functions: A composite function is created when one function is substituted into another function.
Inverse of Functions: These functions are also onto and one to one(1-1) as well. The domain becomes the range and the range becomes the domain.
