Page 18 - Mathematics_Form_3

Relations

Test few points which do not lie on Example 1.11
the dotted line. For instance, from
the left region, choose the points Let R = {(x, y ): x + y ≤ 2 and y ≤ 2}
( 2,2)− and (2, 5)− , while from be a relation of real numbers. Draw
the right region choose the points the graph of R and state its domain
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( 2,6)− and (2, 2)− . In this case, the and range.

points ( 2,6)− and (2, 2)− satisfy the Solution
relation R, and hence they are in the Draw the lines, the lines divides the
required region, while the points xy-plane into distinct regions. A point
(−2, 2) and (2, −5) do not satisfy is selected from each region and
the relation R. substituted into the given inequalities.
Shade the required region which contain The region containing the point that
points that satisfy relation R as shown satisfies all inequalities is then shaded.
in the following figure. For instance, the points ( − 2, − 2),
(4, 1), (3, 4), and (−3, 3) are chosen
y
(-2, 6) from different regions in the following
6
figure. Upon testing, ( − 2, − 2) satisfies
5
y=-2x+1 all inequalities. Therefore, the region
4
contains point ( − 2, − 2) is shaded.
3 Again, test the second inequality
(-2, 2)
2 and shade the wanted region. The
1 region where the shading intersect is
x the required region as shown in the
-4 -3 -2 -1 0 1 2 3 4 5
-1 following figure.
(2,-2)
-2 y
7
-3
6
-4 x+y=2 5
(2,-5) (3, 4)
-5 4
(-3, 3)
3
y=2
From the graph, as the line extends 2
1 (4, 1)
infinitely in both directions, all values x
of x and y are involved. Therefore, -4 -3-2-1 0 1 2 3 4 5 6 7 8 Mathematics for Secondary Schools
}
domain = { :xx∈ , (-2,-2) -1

-2
}
range = { :yy ∈ .
-3
-4
-5
Some linear relations involve more than
one inequality. In this case, the solution is Therefore, from the graph, the domain
}
the set of all ordered pairs which satisfy
of is { :xx∈ and the range is
all the inequalities in the given relation. { y : y ≤ 2} .

Student\s Book Form Three 11

18/09/2025 09:58:39
MATHEMATIC F3 SB.indd 11
MATHEMATIC F3 SB.indd 11 18/09/2025 09:58:39