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NUMBER AND ALGEBRA
CONTENT STANDARDS:
1. simple geometric concepts and notations.
2. perpendicular and parallel lines, and angles formed by parallel lines cut by a transversal.
TYPES OF FUNCTIONS
TYPES OF FUNCTIONS
What is a Function?
A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.
WHAT MAKES A RELATION A FUNCTION?
WHAT MAKES A RELATION A FUNCTION?
On the other hand, a function is actually a “special” kind of relation because it follows an extra rule. Just like a relation, a function is also a set of ordered pairs; however, every x-value must be associated to only one y-value.
A relation that is not function
A relation that is not function
Since we have repetitions or duplicates of x-values with different y-values, then this relation ceases to be a function
A relation that is a function
A relation that is a function
This relation is definitely a function because every x-value is unique and is associated with only one value of y. Because of this specific property, a relation behaves well. As a result, a function can be thought of as a well-behaved relation.
Types of functions
Types of functions
One-to-one function: A function f: A →B is said to be one-to-one if all the elements in A can be mapped with the elements in B. The other name for this type is the injective function.
Onto function: In a function f: A →B, if all the elements of B are images of some elements of A, the function is termed as an onto function.
Many to one function: When more than one element of A is connected to the same element of B in a function f: A →B, it is said to be many to one function.
Bijective function: A function that is both one-to-one and onto at the same time is called a bijective function.
Constant function: A constant function f(x) = K, where K is a real number. For different values of the domain, the same range value for K is obtained.
Identity function: A function where each element of set B gives the image of itself as the same element is called an identity function.
There are a few algebraic functions such as linear function, objective function, quadratic function, cubic function and polynomial function. These functions are based on the degree of the algebraic functions.
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