Page 16 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

With the information obtained above, the graph of y = x – 2x – 5x + 6 may
3
2
be drawn as shown below.
1
y
3
2
y = x – 2x – 5x + 6
6

x
–2 0 1 3

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

As x → –∞ , y → –∞.
The value x = 1 (repeated) shows that the curve touches the x-axis at the point
x = 1.
The minimum point is at (1, 0).
The maximum point lies in the interval [–1, 1].

3
The graph of y = x – x – x + 1 is as shown below.
2
y
3
2
y = x – x – x + 1
1

x
–1 0 1

Graphs of power functions

n
(a) If n is a positive integer (n  Z ), the curve y = kx meets the x-axis at y = 0, i.e. x = 0.
n
+
If n is even, the curve touches the x-axis at the origin (0, 0).
The curve has a minimum point if k . 0 and a maximum point if k , 0.

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01a STPM Math T T1.indd 13 3/28/18 4:20 PM