FUNCTIONS

FUNCTIONS

1. Definition: Every element in X should correspond only one elemnt in Y

2. Finding the values of a functions

   • To find the value of a functions we should solve the given formula
   • Let say f(x) = 3x - 4 So if x is equal to 2 then f(2) = 6 - 4 = 2

3. To be a function

   • Inputs should pair with only one element of the range.
   • Every element of inputs should have a image.

4. Domain= Input

   • Range = Codomain
   • Image= The set of all output values the function produces
     • For this set Range= Image

5. Types of Functions

   • Linear Function
     • A function that has either one or two variables without exponents.
   • Equality of Two Functions
     • Two functions that has the same domain and range.
     • If f= {(1,-1),(2,1),(3,3)} and g(x)= 2x-3 then f(1) = -1 g(1) = 2-3 = -1 f(2) = 2 g(2) = 4-3 = 1 f(3) = 3 g(3) = 6-3 = 3
   • Piecewise Defined Functions
     • Function that should use more than one formula to define the output.
   • Even Function, Odd Functions and Neither Even nor Odd Functions
     • Even Functions
       • The power of x must be even numbers f(x) = f(-x) The graph of an even functions is symmetrical to y- axis
     • Odd Functions
       • f(-x) = -f(x) The power of x must be an odd number The graph of an odd function is symmetrical to origin
     • Neither Even nor Odd Functions
       • A functions that isn't even or odd.
   • Into Functions and Onto Functions
     • Into Function
       • Function that at least one element in range that isn't the image of domain.
     • Onto Function
       • Function that every element in range should be image of the domain.
   • One-to-One Functions
     • Function which the image of every element in the domain is different than one another.
   • Constant Function
     • Function that all inputs has the same image.
   • Unit (Identity) Function
     • Function which returns the same value, of the argument that has been used.

6. Operations on Functions

   • We can add, subtract, multiply, and divide functions

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