RELATIONS

If you have two sets, say A and B, every subset of A X B is a relation from A to B 

A relation is used to describe certain properties of things, that is why certain things may be connected in same way this is called a relation.

                                                         

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And x = 2
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Domain of R-1 = { x : x

Range of R-1 = {y: y> -2}

Solution

R ={(-1, 1) (1, -1) }  and    -1={(1, -1) (-1, 1) }

 

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FUNCTION

A function is a set of ordered pairs which relates two sets such that to each element of one set there is only one element of the second set

 

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Example

Represent the following set of ordered pairs in a pictorial diagram

        A                                          B

 


 

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A function whose graph is such that any line drawn parallel to the x – axis at any point cuts it at only one point is one-to-one function

 Example

Write the expression of a function ‘ double plus one’

   

Exercise 

 

Write each of the following function in the form f: x     http://www.jipime.com/tz/Doc4_files/image015.gif  f(x) use any functions symbol to represent the functions


Find the value of the function for each given value of x

   

 

 

  
 

 

   

Draw the graph of h(x) = 3x-4

Table of values of function 

 X

 -1

 0

 1

h(x)

 -7

 -4

 -1


 

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QUADRATIC FUNCTIONS

   

 

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The shape of the graph of f(x)=ax2+bx+c is a parabola

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The line that divides the curve into two equal parts is called a line of symmetry [axis of symmetry]

The point [0,0] in f(x)=x called the turning point (vertex).

If “a” is positive the turning point is called minimum point (least value).

If a is negative the turning point is called maximum point.

 

PROPERTIES OF QUADRATIC FUNCTIONS

             

                        

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Exercise 

Draw the graph of the function y=x2-6x+5 find the least value of this function and the corresponding value of x

Solution

 

                 

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Find the maximum value of the function.

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