Page 17 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions
(b) {(–2, 4), (–1, 1), (1, 1), (2, 4)} 13. Given a function h(t) = 5 − AB t . Find
(c) (a) h(9) (b) h(0.25) (c) h(4x )
2
Input value, x 1 2 3 4 5
Output value, y 12 24 36 48 60 14. Given a function g(x) = −2x + 15. Find the object
which has an image
(a) −5 (b) x 2
(d) y = −4x + 2 (e) y = (x + 2) + 3 (c) which is the same as the object under the
2
3
(f) y = (g) y = |x + 4| mapping of the function g.
(a) 3 Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
x + 5
2
2
(h) The total surface area of a cube: L = 6x , where 15. A function f is defined as f : x → x – 2x – 10 for
x is the length of each side of the cube. x . 0. Find the value of the object which is mapped
to itself.
8. For each of the following graphs of functions,
determine the domain and range. 16. Given a function g : x → |4x – 3|. Find
(a) (b) (a) the image for x = −1 and x = 2,
y y (b) the values of object which the image is 9,
15 9 (c) the values of x so that g(x) = x.
Form 4
7
17. Given f : x → |2x – 7|. Find
(a) f(2),
3 (b) the values of x so that f(x) = 5.
x x
0 8 –6 0 1 18. The following diagram shows the graph of function
y = f(x), where f(x) = |3x + 6|, for –3 < x < k.
9. The following diagrams show the representations of y
y = f(x), where f(x) = −x + 2, for different domains.
(a) (b) 9
y y
y = f(x) y = f(x) y = f(x)
h
x
2 0 k
x –3
0 0 x
(a) Find the values of h and k.
(c) y (b) Hence, state the corresponding range of f(x) for
y = f(x) the given domain.
(–4, 6)
(–3, 5) 19. The value V, in RM, of a car n years after purchased
(–2, 4)
(–1, 3) is given by
(0, 2) 76 000
V(n) = + 1 000
x n + 1
0 (a) What is the value of the car, in RM, when it was
State the corresponding range for the given domain. newly purchased?
(b) Determine the value of the car, in RM, 7 years
10. Sketch a graph for each of the following functions. after purchase.
Hence, state the corresponding range for each (c) In how many years will the value of the car
domain given. decrease to RM20 000?
(a) f(x) = |x| for the domain –2 < x < 2. (d) Is V(n) a function? Explain your answer.
(b) f(x) = |x + 2| for the domain –3 < x < 3.
(c) f(x) = |x – 5| for the domain 0 < x < 8.
(d) f(x) = |2x + 3| for the domain – 4 < x < 2.
11. Given a function f(x) = 5 − 2x. Find the image when 1.2 Composite Functions
the object is
1
(b) t (c) t + 1 A Describing the outcome of
2
composition of two functions
12. Given a function g(y) = 3y + 1. Find the image when
the object is 1. In the following arrow diagram, the output z is
(a) 0 (b) 3x (c) 2z − 1 ‘the value of input x multiplied by 2 and added
to 5’.

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