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FUNCTIONS - Coggle Diagram
FUNCTIONS
Types of Functions
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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.
Expressed as
f : A → B for any a, b ∈ A ,
for a≠b, if f(a)≠f(b) is satisfied, then f is a one-to-one function
for f(a) = f(b), if a=b is satisfied, then f is a one-to-one function
Into Function
Lets say f : A → B is a function.and If f(A) ≠ B, f is an into function.
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Linear Function
For any real numbers a and b, f :R → R , f(x) = y = ax+b is said to be linear function.
If f is a linear function, then its graph is a line.
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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. These functions are called piecewise functions
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GRAPHS OF FUNCTIONS
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Vertical Line Test
To determine whether a graph represents a function, vertical lines (lines parallel to y axis) can be drawn on the graph. The vertical lines must intersect the graph at one and only one point. If the vertical lines intersect the graph at one point for all real numbers, then the graph represents a function. If the vertical lines intersect the graph at two or more points, then the graph doesn’t represent a function.
Inverse of a Function
For a function f: X → Y to have an inverse, it must have the property that for every y in Y, there is exactly one x in X such that f(x) = y.
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What is Functions
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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if x ∈ A, y ∈ B then the relation can be expressed as f : x → y , f(x) = y
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Functions can be considered mechine like operations; you give a input, have a rule as function and then you get a output
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