MATHEMATICS FORM THREE SUBJECT NOTES
CHAPTER : 1  RELATIONS AND FUNCTIONS

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.      And x = 2 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) }   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 Example

Represent the following set of ordered pairs in a pictorial diagram

A                                          B 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 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          QUADRATIC FUNCTIONS  The shape of the graph of f(x)=ax2+bx+c is a parabola 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    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   Find the maximum value of the function.     www.learninghubtz.co.tz

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