Page 19 - Mathematics_Form_3

Relations

2 _
4 _
Example 1.12 the point of intersection is , .
(
)
3
3
Since the lines are dotted, the values
Find the expression of the relation at the point of intersection are not
given by the following graph. State its included. Therefore, the greater than
domain and range.
sign should be used. Hence, the range
FOR ONLINE READING ONLY
y  4 
of R is yy >  : , y∈   .
5  3 
4
y=2x
3
Exercise 1.4
2
1 Draw the graph of each of the following
x+y=2 relation R and determine domain and
-4 -3 -2 -1 0 1 2 3 4 x
range.
-1
1. R = {( , ):xy y ≤ 2x + } 3
-2

2. R = {( , ):xy y >− 3x + } 5

Solution
Choose any point in the shaded region, 3. R = {( , ):xy y ≥ } 4
preferably a point on x-axis, y-axis 4. R = {( , ):xy x <− } 2
or the origin (0, 0). For instance,
(0, 4) substituting x = 0 and y = 4  1 
in the equations y = 2x and x + y = 2 , 5. R =   ( , ):xy y < 2 x − 1  
Hence, 4 > 0 (true) and 4 > 2 (true).
2x −
Thus, the shaded region represents 6. R = {( , ):xy y ≥ y <− + } 1 } 3
Mathematics for Secondary Schools x + y > 2. Therefore, the relation R y ≤ 12 and x y−> } 1 x + } 1 2y ≤ 1 and x − 2y <− } 1 } 1
the set of all ordered pairs (x, y) of
x
{( , ):xy
7. R =
real numbers such that y > 2x and
x y− >
{( , ) : 2xy
8. R =
is given by R = {(x, y ) : y > 2x and
1 and x −
{( , ) : 2xy
R =
2y <−
x y− >
x + y > 2} . The domain of the relation

R = {(x, y ): y > 2x and x + y > 2} is
9. R =
{( , ) :3xy
12 and x y−>
the set of all real numbers, because as
{( , ) :3xy
x +
the lines extend to infinity, all values 2R =
of x are involved. To find the range
of R, take all values of y which are in
represented by the graphs. Use the
the shaded region. From the graph, the In questions 10 to 15, find the relations
values of y start at a point of intersection graphs to find the domain and range
of the two inequalities. In this case, of each relation.
12 Student\s Book Form Three

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MATHEMATIC F3 SB.indd 12 18/09/2025 09:58:39
MATHEMATIC F3 SB.indd 12