Page 42 - Mathematics_Form_3

Functions

13. y For example, if x = 11, for the function
f (x ) = 3x + 1, becomes
4
f (11 ) = 3 × 11 + 1 = 34.
3 3
2
x=-(y-2) +1 Likewise, if ( ) = 16, the value of can
2 2
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be determined by solving the equation
3 + 1 = 16 giving = 5.
1 1
A function can be represented graphically
-3 -2 -1 0 0 1 2 3 x
() . Then, the function
by setting y = fx
-1
() 3x=
fx + 1can be written as = 3 +1.

14. y The equation tells us that the values
4 4 of depend on the values of x. Thus,
the values of can be calculated by
3 3 substituting the corresponding values
2 2 of x.
The graph of a function ( ) is the same
1 1
as the graph of the equation = ( ). If
the point ( , ) satisfies the equation,
-1 0 1 2 3 4 x
then a represents the value of and
-1
represents the value of y and it is written
-2 as ()fa = . b

-3 The graph of y = 3x + 1 can be drawn
on the -plane as shown in Figure 2.3.
-4

y
Function notation
Consider a function which maps 2
onto 3 + 1. In mathematical language, y=3x+1
it is denoted by : → 3 +1, and is read 1
as ʻ is a function that maps x onto Mathematics for Secondary Schools
3x + 1̕ . Each value of is obtained by x
multiplying each value of x by 3 and -2 -1 0 1 2
adding 1. -1
The previous function notation can also
be written as () 3fx = x + 1 and read as -2
ʻ of x equals 3x plus 1̕ . The value of
( ) can be found by substituting the
values of . Figure 2.3: Graph of f(x ) = 3x + 1

Student\s Book Form Three 35

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MATHEMATIC F3 SB.indd 35 18/09/2025 09:58:51
MATHEMATIC F3 SB.indd 35