Page 15 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

(b) f(x) = –2x + 3x + 1 can be expressed as
2
2
f(x) = –2(x – 3 x) + 1
1 2
9
1
2
= –2 x – 3 2 – 16  + 1, by completing the square
4
1
2
= –2 x – 3 2 + 9 + 1
8
4
2
1
= –2 x – 3 2 + 17 .
8
4
The graph cuts the y-axis when x = 0, i.e. y = 1.
As x → `, y → –`.
Similarly when x → –`, y → –`.
When x = 3 , y = 17 is the maximum value of f(x).
4 8
2
Hence the graph of y = –2x + 3x + 1 is as shown below.
y
17
–
8
2
y = –2x + 3x + 1
1

x
0 3
–
4

Example 7

Sketch the graphs of
2
3
2
(a) y = x – 2x – 5x + 6 (b) y = x – x – x + 1
3
2
3
Solution: (a) Let y = x – 2x – 5x + 6
= (x + 2)(x – 1)(x – 3)
2
3
The graph of y = x – 2x – 5x + 6 is in the form .
The graph crosses the x-axis when y = 0,
i.e. (x + 2)(x – 1)(x – 3) = 0.
Hence, x + 2 = 0, x – 1 = 0 or x – 3 = 0.
i.e. x = –2, 1 or 3.
The graph crosses the y-axis when x = 0, i.e. y = 6
As x → ∞ , y → ∞.
As x → –∞ , y →–∞.

The maximum point must lie in the interval [–2, 1].
The minimum point lies in the interval [1, 3].

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01a STPM Math T T1.indd 12 3/28/18 4:20 PM