Page 59 - Mathematics_Form_3

Functions

y  1 
8. y =  x +  for n ≤ x < n + 1, where n is an integer.
1  2 
 1 
y =  x +  for n ≤ x < n + 1, where n is an integer.
-4 -3 -2 -1  0 2  1 2 3 x
FOR ONLINE READING ONLY
-1 9. The function ()fx is defined as
follows:
-2  − 1 if x < 0
}
( ) =

Domain = { :xx∈ and fx  0 if x = 0

range = {y : − 1 < y ≤ 0} .  1 if x > 0
Find: (a) (3)f and ( 2)f −
Exercise 2.6
(b) sketch the graph of ()fx
1. Find the value of: (c) Find the range of ()fx
 23
(a)   4   (b) 0.1    10. Sketch the graph of

3 x for n − <
y =  1 x ≤ n where n is an integer.

(c) −   1.01  (d) 102   
3 x for n − <
y =  1 x ≤ n where n is an integer.and state its

In questions 2 to 8 sketch the graph domain and range.
each of the given functions:
2. f ( )x = 2 forn n − 1 ≤ x < , n n is a positive integer.
f ( )x = 2 forn n − 1 ≤ x < , n n is a positive integer. Absolute value functions
The absolute value of a number, say x,
3. f ( )x = 3 forn n − 1 ≤ x < , n n is a positive integer.
is its value without regarding its sign.
f ( )x = 3 forn n − 1 ≤ x < , n n is a positive integer. It is denoted by two vertical bars .

x
, if 0 ≤
−  1, if x ≥ 3 x < x < 2 3 For instance, both 2 and 2− equal 2,

Mathematics for Secondary Schools 6. ux =  0 if x < 0 symbol. For instance, ()fx = x which
4, if 2 ≤
4. fx =
( )
x −
since both 2 and 2− are 2 units away


from zero on the number line.

An absolute value function is a function
( ) =

whose definition contains an algebraic
1, where n
gx x x  for n ≤ x < n + 5. gx x x  for n ≤ x < n + 1, where n is an integer.
is an integer.
( ) =
expression within the absolute value

()

means
1 if x ≥
0


fx
() =

x 
x
−
if x <
0

1, where n
gx  for n < x ≤ 7. (a) ( )gx =  for n < x ≤ n + 1, where n is an integer. x if x ≥ 0
( ) =
n +
is an integer.
x 
Example 2.26
(b) ( )hx =  for n ≤ x < n + 1, where n is an integer. x and state
x 
Sketch the graph of ()fx =
( ) =
hx  for n ≤ x < n + 1, where n is an integer. its domain and range
x 
52 Student\s Book Form Three
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MATHEMATIC F3 SB.indd 52 18/09/2025 09:59:01
MATHEMATIC F3 SB.indd 52