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FUNCTIONS, References - Coggle Diagram
FUNCTIONS
ONE TO ONE FUNCTIONS
If the image of each element in the domain is different than one another, the function is called a one-to-one function.
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EQUAL FUNCTIONS
Let f: A --> B and g: A --> B be two functions, if f(x) = g (x) then f and g are called
equal functions
In order to decide on the equality of two functions, the requirements are as follows;
- The domain and the range of the functions must be equal.
- The image of each element of the domain under both functions must be equal.
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.
EXAMPLE:
f: R --> R, f(x)=(m-2)x+m+1 is a constant function;
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IDENTITY FUNCTIONS
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Let A be a set. The function I: A --> A is defined by I(x) for all x ∈ A is called identity function .
ONTO FUNCTIONS
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If a function’s image is equal to the
range, the function is called an onto function
LINEAR FUNCTIONS
For any real numbers a and b,
f :R --> R , f(x) = y = ax+b is said to be linear 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. Such functions are called piecewise functions.
EXAMPLE: Evaluate each piecewise function for x = –1 and x = 3. 3x2 + 1 if x < 0 g(x) = 5x –2 if x ≥ 0
Because –1 < 0, use the rule for x < 0. ANSWER: g(–1) = 3(–1)2 + 1 = 4
Because 3 ≥ 0, use the rule for x ≥ 0. ANSWER: g(3) = 5(3) – 2 = 13
GRAPHS OF FUNCTION
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The set of the points in the analytic plane corresponding to the elements of a function is the graph of
this function.
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INVERSE OF A FUNCTION
Example: 
Inverse functions, in the most general sense, are functions that "reverse" each other.
COMPOSITION OF FUNCTIONS
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The term composition of functions refers to the combining together of two or more functions in a manner where the output from one function becomes the input for the next function.
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INTO FUNCTIONS
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Let f: A --> B be a function. If (A) ≠ B, f is said to be an into function
DEFINITION OF A FUNCTION
By definition, 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).
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References
Math Booklet
shelovesmath.com
onlinemathlearning.com
en.wikipedia.org
khanacademy.org
sfu.ca
mathinsight.org sejucırylav.wowinternetdirectory.com