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FUNCTIONS - Coggle Diagram
FUNCTIONS
INTO FUNCTIONS & ONTO FUNCTION
ONTO FUNCTION
If A and B are the two sets, if for every element of B, there is at least one or more element matching with set A, it is called the onto function.
INTO FUNCTION
Into function is a function in which the set y has atleast one element which is not associated with any element of set x. Let A={1,2,3} and B={1,4,9,16}. Then, f:A→B:y=f(x)=x2 is an into function, since range (f)={1,4,9}⊂B.
EVEN FUNCTIONS & ODD FUNCTIONS
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 FUNTION
Some examples of odd functions are y=x3, y = x 3 , y=x5, y = x 5 , y=x7, y = x 7 , etc. Each of these examples have exponents which are odd numbers, and they are odd functions.
OPERATION ON FUNCTION
Addition. We can add two functions as: (f + g)(x) = f(x) + g(x) Example: ...
Subtraction. We can subtract two functions as: (f – g)(x) = f(x) – g(x) Example: ...
Multiplication. (f•g)(x) = f(x)•g(x) Example: f(x) = 3x – 5 and g(x) = x. ...
Division. (f/g)(x) = f(x)/g(x) Example:
WHAT İS THE VALUE OF FUNCTION
f(x)=mx+b. f(x) is the value of the function. m is the slope of the line. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane. x is the value of the x-coordinate.
DEFINITION OF A FUNCTION
an expression, rule, or law that defines a relationship between one variable
CONSTANT FUNCTION
a constant function is a function whose (output) value is the same for every input value. For example, the function y(x) = 4 is a constant function because the value of y(x) is 4 regardless of the input value x
EQUALİTY OF TWO FUNCTION
We say two functions f and g are equal if they have the same domain and the same codomain, and if for every a in the domain, f(a)=g(a).
PIECEWISE DEFINED FUNTIONS
piecewise defined functions ile ilgili görsel sonucu
A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1.
ONE-TO-ONE FUNCTION
A one-to-one function is a function of which the answers never repeat. For example, the function f(x) = x + 1 is a one-to-one function because it produces a different answer for every input.
PIECEWISE FUNCTIONS
A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value, Additional piecewise functions include the Heaviside step function, rectangle function, and triangle function.
ZERO OF A FUNCTION
The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.
COMPOSITION FUNCTION
function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g is applied to the result of applying the function f to x.