Page 16 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions
Mark (✓) for the characteristics of a function which (c) (d)
maps set A to set B. y y
(a) Each input in set A must be matched
with one output in set B.
x x
(b) There may be two or more inputs in O O
set A which can be mapped to the
same output in set B.
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(c) One input in set A can be mapped to 4. (a) In each of the following diagrams, set B
two or more different outputs in set B. contains the images of some of the objects in
set A.
(i)
2. The following arrow diagrams show the relations x f(x)
between two sets, X and Y. 3 Form 4
(a) times 2 5 27
1 2 –5 125
–3
2 4
6 Set A Set B
4 8
(ii) x h(x)
Set X Set Y
0 1
1 2
3 4
(b) multiple of 5 6
2
Set A Set B
2 4
3 6 Write the relation between set A and set B
using function notation.
2
(b) The area, A of a circle with radius r units is πr .
Set X Set Y Write the relation between the area of the circle
and its radius using function notation.
(c) Complete the following.
(c) Equation Function
p a (i) y = 2x + 3x − 1
2
q
r b (ii) y = sin x
s
5. For each of the following reciprocal functions,
Set X Set Y
determine the value of k.
5 7
(a) f(x) = – , x ≠ k (b) g(x) = , x ≠ k
Determine whether the relations are functions. State x x + 3
your reasons. (c) h(x) = 3 , x ≠ k (d) p(x) = 1 – 1, x ≠ k
4x – 1 3x + 2
3. By using the vertical line test, determine whether the
relations in the following graphs represent y as a 6. Determine whether the following statements are true
function of x. Justify your answers. regarding the graph of function f(x) = |x|.
(a) The graph contains all positive values of x.
(a) (b) (b) The y-axis is the axis of symmetry of the graph.
y y (c) The entire graph lies above the x-axis.
x 7. Determine the domain and range for each of the
O following functions.
(a)
x x p
O
y q
z r
Set A Set B
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