Page 30 - Mathematics_Form_3

Relations

y Example 1.27
3
Draw the graph of the inverse of the
y = x
2 relation R = {(x, y ) : y = 3x} .

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1 Solution
From the equation y = 3x, interchange
-2 -1 0 1 2 3 x the variables x and y to obtain x = 3y.
-1 Writing y in terms of x, gives y = .
x _
3
x _
−1
-2 Hence, R = (x, y ) : y = and its
{
}
3
graph is shown in the following figure.
-3
y
Figure 1.10: Graph of the inverse relation 3
–1
R = {(x, y ) : y < x}
2
x
y =
Example 1.26 1 3
x
Consider the relation given by -3 -2 -1 0 1 2 3
R = {(x, y ) : y > 2x} . Its inverse is -1

x _
R = (x, y ) : y < . The graphs
−1
{
}
2
of R and R are shown on the same -2
−1
pair of axes in the following figure. -3
y
4
y=x
3 Example 1.28
2
Draw the graph of the inverse of the
1 relation R = {(x, y ): y ≤ 0 and y ≥ x} , and

x

−1
-4 -3 -2 -1 0 1 2 3 4 then find the domain and range of R .
-1
Solution
-2 Mathematics for Secondary Schools
Note that, after interchanging x and y,
-3
and rearranging the equation, gives:
-4
R = {(x, y ): x ≤ 0 and y ≤ x} .
−1
From the graph, it can be observed Therefore, the graph of R is as shown
−1
that, the graph of R can be obtained in the following figure.
−1
by reflecting the graph of R about the
line y = x.

Student\s Book Form Three 23

18/09/2025 09:58:46
MATHEMATIC F3 SB.indd 23 18/09/2025 09:58:46
MATHEMATIC F3 SB.indd 23