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FUNCTION - Coggle Diagram
FUNCTION
Unit Functions
In number theory, the unit function is a completely multiplicative function on the positive integers defined as: It is called the unit function because it is the identity element for Dirichlet convolution.
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Constant Function
A constant function is a function which takes the same value for f(x) no matter what x is. When we are talking about a generic constant function, we usually write f(x) = c, where c is some unspecified constant.
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Linear Function
In Mathematics, a linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line.
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One-to-One Function
If the image of each element in the domain is different than one another, the function is called a one-to-one function. One-to-oneness can be denoted as 1-1.
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Into Functions
- An into function is a type of function where one or more elements of the codomain will not have a pre-image in the domain.
- The range of an into function will be a subset of the codomain. The range will not be equal to the codomain.
- The vertical line test is used to check if a given graph is a function or not. If the graph intersects with the vertical line at exactly one point, it will be a function. : :
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Onto Function
- We can define onto function as if any function states surjection by limit its codomain to its range.
- The domain is basically what can go into the function, codomain states possible outcomes and range denotes the actual input of the function.
- Every onto function has a right inverse.
- Every function with a right
inverse is a surjective function.
- If we compose onto functions, it will
result in onto function only.
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Even Functions
A function is called an even function if its graph is unchanged under reflection in the y-axis. Suppose f(x) is a function such that it is said to be an even function if f(-x) is equal to f(x).
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Odd Functions
A function f is said to be an odd function if -f(x) = f(-x), for all value of x. In Mathematics, the functions even and odd are those that satisfy specific symmetry relations, with respect to considering additive inverses. They are fundamental in the analysis of mathematics, power and the Fourier series.
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Graphs of Functions
The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function if a special case of the graph of an equation.
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