Page 57 - Mathematics_Form_3

Functions

(c) The function gives only the values y
–2, 0 or 2 for any value of x. 4
Therefore, the range is {–2, 0, 2}. 3
()
(d) fx is not a one-to-one function, 2
FOR ONLINE READING ONLY
since ( ) 2f − = f ( ) 1− = − 2 . 1

-4 -3 -2 -1 0 1 2 3 4 x
Example 2.23 -1
Given the function f defined as -2
 − 3 if x ≤ 1 -3
fx  1 if 1 x<≤ 2 -4
( ) =

 x
 4 if 2 <
Draw the graph of and hence state its Domain = {x : x ∈ ℝ} and
domain and range. range = {− 3, 1, 4} .

Solution
Let y = f (x), it implies Greatest and least integer function

 − 3 if x ≤ 1 Greatest and least integer function is
a form of a step function. The greatest
y =  1 if 1 x<≤ 2 integer function is a function that gives

 4 if 2 < x
 the greatest integer less than or equal
For y = − 3, draw a horizontal arrow to a given number. The greatest integer
with a solid dot starting from (1, −3) less than or equal to a given number,
.

towards the negative x values (since say x is denoted by x  The function
x
f defined by ()fx =  is called the

x ≤1 ).
Mathematics for Secondary Schools at y = 1 which starts from (1, 1) to The least integer function is a function
greatest integer function or the floor
For y = 1, draw a horizontal line segment
function.
(2, 1). At (1, 1), the line segment should
that give the least integer which is
have an open circle since x = 1 is not
greater or equal to the given number.
included ( 1 < x ) and at (2, 1) should
The least integer which is greater
have a solid dot since 2 is included
or equal to a given number, say x is
( x ≤
) 2 .
denote by x  . The function f defined

x
()

For y = 4, draw a horizontal arrow by fx =  is called the least
starting at (2, 4) towards the right with
integer function or the celling function.
an open circle at x > 2. The graph of the The following table shows examples
function is as shown in the following of different values substituted to the
figure. greatest and least integer functions.

50 Student\s Book Form Three

18/09/2025 09:58:59
MATHEMATIC F3 SB.indd 50
MATHEMATIC F3 SB.indd 50 18/09/2025 09:58:59