Page 6 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

Set P is the domain and set Q is the codomain. The set of images {1, 4, 9} is the range of this function.

P 'is the square of' Q
1
–2
–1 1
1 4
2 9
3 16 Range
Domain Codomain
Figure 1.3

Example 1

X Y
–2
0
–1
1
0
2
1
5
2
f
(a) Show that the diagram above defines a function f from set X to set Y.
(b) Find f(x).
(c) State the domain of f and its range.
Solution: (a) For each element x in set X, there exists a unique image y in set Y. Hence, f
can be defined as a function from set X to set Y.
(b) f(0) = 1 = 0 + 1
2
f(–1) = f(1) = 2 = 1 + 1
2
f(–2) = f(2) = 5 = 2 + 1
2
Hence, f(x) = x + 1.
2
(c) Domain of f is {–2, –1, 0, 1, 2}
Range of f is {1, 2, 5}

Example 2

Determine whether each equation defines y as a function of x. If so, determine whether the function is
one-to-one.
(a) y = x + 2,
2
(b) y = x + 3x + 2,
(c) y = x – 2.
2
Solution: (a) y = x + 2
For each value of x  R, the value of y is unique.
Thus y is a function of x.
No two values of x  R have the same image.
Thus the function is one-to-one.

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01a STPM Math T T1.indd 3 3/28/18 4:20 PM