Page 20 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

The graph of y = |x – 3x + 2| can be drawn by reflecting the section of the graph
2
that is below the x-axis, as shown below.
1
y
2
2 y = x – 3x + 2
1

x
0 1 2

Example 11

Sketch the graph of y = |2x – 3|.
By drawing the graph of y = x on the same diagram, determine the values of x such that |2x – 3| . x.
Solution: |2x – 3| = 0 when x = 3 .
2
The graph of y = |2x – 3| is symmetrical about x = 3 .
2
When x = 0, y = 3.
When x = 3, y = 3.
The graph of y = |2x – 3| is as shown below.

y
y = x
3 y = 2x – 3 A

B

x
0 1 3 _ 2 3
2
Notice that the graph of y = x intersects the graph of y = |2x – 3| at two points,
A and B.
At A, 2x – 3 = x
x = 3

At B, –(2x – 3) = x
–2x + 3 = x
3x = 3
x = 1

Hence, from the graph, |2x – 3| . x if x , 1 or x . 3.

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01a STPM Math T T1.indd 17 3/28/18 4:20 PM