Function

Concept Explanation

Functions are rules which assign exactly one output for one input. It is connecting independent variables to dependent variables.

Subtopics

Definition of a Function

A function is a specific type of relationship or rule that assigns each input value to exactly one output value.

Notation

Function is denoted as f(x) and read as f of x, where f is the name of the function,f(x) gives value on y axis or y in genral. In the function f(x)= 2x, 2x is the rule to calculate f(x).

Domain and Range

Domain is set of possible values of input i.e. x and x axis. Range is set of possible values of output i.e. f(x),y and y axis.

Graph of a Function

  • For f(x)=2x
  • First we will take 3 values such that x and f(x) i.e. y are easy to plot on graph
  • For x=1
  • f(x)=y= 2×x
  • f(1) =2 here the variable x is changed with value of x this does not change the function. f(1) can be useed as value too.
  • For x=2
  • f(x)=2×2
  • f(2)=4
  • For x=3
  • f(x)=2×3
  • f(3)=6
  • and then we will plot the points which we got as (1,2),(2,4),(3,4).

    • graph of f(x)=2x for 3 values of 1,2,3

    test of a function

    1.To test whether a relation is a function or not we use verticle line test in which we take a verticle line and trace alnog the graph if we have the line cutting the graph at two points at any point it is not a function.

    2.We can test a relation for a function much faster than verticle line using arthmetic but for that you need to build intuition which we will build together.

    History Corner

    The concept of function was not discovered but rather it evolved.Although the term was introduced by Gottfried Leibniz in 1673.

    Extras Corner

    1. is f(x)=√x a function or not?
    2. what are properties of functions?