Page 19 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

The graph of y = 2x – 1 is as shown below.
x + 1
1 The asymptotes to the curve are y = 2 and x = –1.
y
asymptote (x = –1)
2x – 1
y = –
x + 1
asymptote (y = 2)

2
x
–1 0 1
–
–1 2

Graphs of functions involving modulus signs

x, x  0,
The absolute value or modulus of x is defined by |x| =
–x, x , 0.
The graphs of y = x and y = |x| are as follows:
y y = x y y = |x |

x x
–3 –2 –1 0 1 2 3 –3 –2 –1 0 1 2 3

Figure 1.14(a) Figure 1.14(b)
For x , 0, the graph of y = |x| is the reflection of the graph y = x about the x-axis, i.e. the graph of y = –x.

Example 10

Sketch the graph of y = x – 3x + 2, noting the points of intersection of the graph with the x-axis.
2
2
On a separate diagram, sketch the graph of y = |x – 3x + 2|.
Solution: y = x – 3x + 2
2
At the point of intersection with the x-axis, y = 0. y
x – 3x + 2 = 0
2
(x – 1)(x – 2) = 0 2 y = x – 3x + 2
2
x = 1 or 2.
At the y-axis, x = 0 ⇒ y = 2. 1
The graph of y = x – 3x + 2 is as shown on x
2
the right. 0 1 2

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01a STPM Math T T1.indd 16 3/28/18 4:20 PM