Page 22 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

Example 13

For x  R, [x] is defined as the greatest integer not exceeding x, 1
5
for example, 3 4 = 2, [3] = 3 and [–1.2] = –2.
2
Sketch the graph of f defined by f(x) = [x] for –2 < x , 3.

Solution: From the definition of [x].
–2 for –2 < x , –1,
–1 for –1 < x , 0,
f(x) = 0 for 0 < x , 1,
1 for 1 < x , 2,
2 for 2 < x , 3.

The sketch graph of f is as follows:
y
y = x[ ]
2
1

x
–2 –1 0 1 2 3

–1
–2

Exercise 1.3

1. Sketch the graphs of
(a) y = 4x + 3 (b) y = –3x + 8 (c) 2y = 5x + 6
2. Sketch the graphs of
(a) y = x + 3 (b) y = 3x – 1 (c) y = –4x + 5x + 2
2
2
2
2
3. Sketch the graphs of
1
3
3
3
(a) y = x – 1 (b) y = –2x + 1 (c) y = – x + 5
2
4. Sketch the graph for each of the following curves, indicating the points of intersection of the curve with
the axes.
2
(a) y = x(x + 1)(x – 2) (b) y = (x + 1) (x – 2)
3
(c) y = (x – 2) 3 (d) y = x – 2x
2
3
(e) y = x – 3x + 2x
5. Sketch the graph of
2
2
2
(a) y = x(1 – x ) (b) y = x(1 – x )
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01a STPM Math T T1.indd 19 3/28/18 4:20 PM