Page 45 - Mathematics_Form_3

Functions

therefore the functions are not one-to- Example 2.8
one, while the horizontal lines drawn Draw the graph of the function defined
in (c) and (d) crosses the graphs once,
1
by ()fx = 2x + and determine if it is
hence the functions are one-to-one.
a one-to-one function.
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Solution
Example 2.6 Choose few values of near the origin

Write the function ʻa number is squared and then use them to calculate the
and then multiplied by 2\ in the form corresponding values of ( ) as shown
f: →f ( ), and then find: in the following table.

(a) f : 2 (b) f (3 ) x − 2 − 1 0 1 2 3

y = f(x) − 3 − 1 1 3 5 7

Solution
The ordered pairs are plotted on the
(a) : fx → 2x 2
xy-plane and joined by a straight line
f : 2 → 2(2) 2 as shown in the following graph.

f : 2 → 8
y
Therefore, : 2f → 8.
7 (3, 7)
2
(b) f (x ) = 2 x 6
f (3) = 2 (3) 5 (2, 5)
2
= 2 (9) 4 y = 2x + 1
= 18 3 (1, 3)
Therefore, f (3 ) = 18. 2 1 (0, 1)
Mathematics for Secondary Schools Consider the function defined by (-2,-3) -1 1 2 3 4 x
Example 2.7
-3 -2 -1 0
(-1,-1)
-2
g(x ) = 3x + 3. Find g(−2).
-3
Solution
-4
gx
() 3x=
3
+
−+
=

63
g ( 2) 3( 2) 3− = −+ In this case, any horizontal line drawn
crosses the graph at only one point which
= − 3 indicates that the function represented by
Therefore, ( 2)g − = − 3. a graph is a one-to-one function.

38 Student\s Book Form Three

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