Page 46 - Mathematics_Form_3

Functions

Example 2.9 1. Divide a number by 5 and add 2.
Draw the graph of the function 2. Add a number to 2 and divide the
fx x and determine if it is a sum by 5.
2
() =
one-to-one function. 3. Square a number and subtract 7.
FOR ONLINE READING ONLY
Solution 4. Subtract 7 from a number and
Select few points on the graph of the square the difference.
2
function ()fx = x as shown in the 5. Subtract a number from 8.
following table. 6. Subtract a double of a number from

x − 3 − 2 − 1 0 1 2 3 6.

f (x) 9 4 1 0 1 4 9 In questions 7 to 10 find the values

The ordered pairs are plotted on the of each of the functions for the given
xy-plane and joined as shown in the values of :
following figure. 7. f (x ) = 2x + 3; x = 1, x = − 2, x = a
y 2
8. C (x ) = − (x − 1) ; x = 3, x = 7
(-3, 9) 9 (3, 9)
9. S (x ) = x ; x = − 1, x = 5, x = 4
2
8
10. K ( ) = 3; = 1, = 7
7
In questions 11 to 18 draw the graph
6
of each function for some appropriate
5
(-2, 4) 4 (2, 4) values of and determine if it is a one-
to-one function:
3
2 11. f (x ) = 2x + 3
(-1, 1) 1 (1, 1) 12. f (x ) = x − 1
(0, 0)
-4 -3 -2 -1 0 1 2 3 4 x 13. f (x ) = − 2
-1
2
14. f (x ) = ( x + 2)
Clearly, a horizontal line drawn on 15. f (x ) = − x − 1
the graph would cross the graph more 16. f (x ) = − x Mathematics for Secondary Schools
2
than once, hence it is not a one-to-one
2
function. 17. f (x ) = x − x + 1
18. f (x ) = 3 − x

Exercise 2.2 In questions 19 to 23 determine which

In questions 1 to 6 write each of the function is one-to-one:
functions in the form 19. f = { ( , ): is a pupil in your
f : x → f (x ). school and y is her first name}

Student\s Book Form Three 39

18/09/2025 09:58:54
MATHEMATIC F3 SB.indd 39
MATHEMATIC F3 SB.indd 39 18/09/2025 09:58:54