Page 9 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions
(c) Complete the following:
Solution
Equation Function In the first diagram, x = 0, f(x) = 2
f(0) = p(0) + q = 2 ......................a
y = 2x + 4
2
In the second diagram, x = 1, f(x) = 5
f(1) = p(1) + q = 5 ......................b
Solution From a, q = 2
(a) g : x → AB x or g(x) = AB x Substitute into b, p + 2 = 5
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4
(b) V : r → —πr 3 or V(r) = —πr p = 3
3
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(c) f : x → 2x + 4 or f(x) = 2x + 4 Try this HOTS question
2
2
The following diagrams show the inputs of x into
Try Question 4 in ‘Try This! 1.1’ a function machine which produces output g(x).
Form 4
SPM Highlights Input x Input x Input x
2
4
0
f f f
7
49
6
–6 –2 2 14
36 Output g(x) Output g(x) Output g(x)
–7
If g(x) = ax + b, where a and b are constants,
2
Set A Set B determine the values of a and b.
The diagram above shows the relationship between Solution
set A and set B. a = 1, b = −2
(a) State the type of relation.
(b) Write the relation using function notation.
Solution (c) Reciprocal functions
(a) Many-to-one relation 1. A reciprocal function is expressed in the form of
(b) f : x → x 2 k
f(x) = —, x ≠ 0, where k is a constant.
x
k
2. The graph of function f(x) = — only approaches,
x
Example of HOTS but does not touch the line x = 0 (y-axis). This
HOTS Question
is because the solution of dividing any numbers
The following diagrams show the inputs of x into a with zero is undefined.
function machine which produces output f(x).
For example, the following diagram shows the
Input x Input x Input x 1
0 1 2 graph of function g(x) = .
x + 1
y
f f f
x = –1

2 5 8
Output f(x) Output f(x) Output f(x) x
0
If f(x) = px + q, where p and q are constants,
determine the values of p and q.

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