1.6.3 Function, SPM Practice (Short Question)

Question 7:
Diagram below shows the function g : x → x – 2k, where k is a constant.

Find the value of k.

Solution:
$\begin{array}{l}\text{Given }g\left(6\right)=12\\ g\left(6\right)=6-2k\\ \text{ 12}=6-2k\\ \text{ 2}k=6-12\\ k=-3\end{array}$

Question 8:
Diagram below shows the relation between set M and set N in the arrow diagram.

(a) Represent the relation in the form of ordered pairs.
(b) State the domain of the relation.

Solution: 
(a) Relation in the form of ordered pairs = {(–4, 8), (3, 3), (4, 8)}.
(b) Domain of the relation = {–4, 3, 4}.

Question 9 (3 marks):
Diagram shows the graph of the function f : x → |1 – 2x| for the domain –2 ≤ x ≤ 4.

Diagram

State
(a) the object of 7,
(b) the image of 3,
(c) the domain of 0 ≤ f(x) ≤ 5.


Solution:
(a)
The object of 7 is 4.

(b)
f (x) = |1 – 2x|
f (3) = |1 – 2(3)|
= |1 – 6|
= |–5|
= 5

The image of 3 is 5.

(c)
|1 – 2x| = 5
1 – 2x = ±5
Given when f(x) = 5, x = –2.

When f(x) = –5
1 – 2x = –5
2x = 6
x = 3

Domain: –2 ≤ x ≤ 3.