Page 10 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions
The expression x + 1 in the denominator of the y
equation cannot be zero.
Hence, x + 1 ≠ 0, which is x ≠ −1.

1 y = –x, x < 0 y = x, x 0
Therefore, the graph of function g(x) =
x + 1 x
approaches, but does not touch the line x = −1. 0
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SPM Tips
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For x → –1, y → ∞, the line x = –1 is known as a vertical
asymptote. Likewise, for y → 0, x → ∞, the line y = 0 Which of the following statements is true regarding

(x-axis) is known as a horizontal asymptote. the graph of function f(x) = | x |? Mark ✓ for the true
statements and ✗ for the false statements. Form 4
(a) The graph has a W shape.
4 (b) The graph has a vertex at the origin, O.
For each of the following reciprocal functions, (c) The equation of the axis of symmetry is x = 0.

determine the value of p. Solution
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(a) f(x) = , x ≠ p (a) ✗ (b) ✓ (c) ✓
x – 2
1
(b) g(x) = , x ≠ p
2x + 5 Try Question 6 in ‘Try This! 1.1’
Solution
(a) x – 2 ≠ 0
x ≠ 2
Therefore, p = 2. B Determining the domain and range of
a function
(b) 2x + 5 ≠ 0 1. In the arrow diagram below, set A is the set
2 x ≠ −5 of passengers who arrived at Kuala Lumpur
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x ≠ – International Airport while set B is the set of
2 reasons for their visit to Malaysia.
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Therefore, p = – .
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Prasert Travelling
Try Question 5 in ‘Try This! 1.1’ Jusuf Habibie
Yashimoto Visiting relatives
Tan Chen Huat Work tour
Louise
(d) Absolute value functions Ahmed Wazir Further studies
Medial
1. An absolute value function, f(x) = | x | can be Pavitra tourisms
defined as Set A Set B
x if x > 0
| x | = –x if x , 0 (a) Set A, which is the set of all possible inputs,

is known as the domain of this mapping.
2. An absolute value or modulus of a real number (b) Set B, which comprises all possible reasons
is the numerical value of the number, without for the passengers’ visit to Malaysia, is
considering its sign. known as the codomain of this mapping.
For example, | 4 | = 4 (c) The seven interviewed passengers gave a set
and | –4 | = –(–4) = 4 of answers consisted of four reasons, which
3. The graph of function f(x) = | x | has a V shape are the output. The output formed the range
with the vertex at the origin, O, as shown in the for this mapping.
following diagram. The y-axis (x = 0) is the axis
of symmetry of the graph.

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