Page 50 - Mathematics_Form_3

Functions

y Example 2.16
Draw the graph of the function
6
f (x ) = 2x + 1.
5
Solution
FOR ONLINE READING ONLY
4 The equation has the form
f(x)=-2x+5
3 f(x ) = mx + c with gradient = 2 and 1
as y -intercept, = f (0) = 1. Therefore,
2
the graph passes through the point
1 (0, 1).

-2 -1 0 1 2 3 4 x The -intercept is obtained from setting
() 0= , that is 2x + 1 = 0, which
-1 fx
1 _
-2 when solved gives x = − . Thus, the
2
graph also passes through the point
1 _
− , 0 as shown in the following
In general, the equation of a linear ( 2 )
function with gradient m passing figure.
through the point x , y is given by y
( 0 0)
the equation f (x ) = m(x − x ) + y .
0 0
3

Example 2.15 2
f(x)=2x+1
Find a linear function with gradient −1 1
which passes through the point (1, 2).
Solution -2 -1 0 1 2 3 x
f (x ) = m(x − x ) + y , where x = 1, -1

0
0
0
y = 2 and m = − 1
0
-2
f (x ) = − 1(x − 1 ) + 2
= − x + 3
Therefore, f (x ) = − x + 3 . Mathematics for Secondary Schools
Example 2.17

Draw the graph of f (x ) = x + 3 and
Remark: The graph of a straight line find its domain and range.
can be drawn if any two points are
known. When an equation is given, the Solution
two points on a graph can be identified Linear equations are easily drawn by
by finding the x and y -intercepts. using x and y-intercepts as shown in
the following table.

Student\s Book Form Three 43

18/09/2025 09:58:56
MATHEMATIC F3 SB.indd 43
MATHEMATIC F3 SB.indd 43 18/09/2025 09:58:56