Functions (Chapter 2) 53
EXERCISE 2F
1 Draw sign diagrams for these graphs:
abc
de f
gh i
jk l
Example 15 Self Tutor
Draw a sign diagram for:
a (x+ 3)(x¡1) b ¡4(x¡3)^2
a (x+ 3)(x¡1) has zeros¡ 3 and 1.
When x=2we have (5)(1)> 0 ,
so we put a+sign here.
As the factors are single, the signs
alternate.
b ¡4(x¡3)^2 has zero 3.
Whenx=4we have¡4(1)^2 < 0 ,
so we put a¡sign here.
As the factor is squared, the signs do
not change.
- 3 1
+ - +
x
3
--x
We substitute any number> 1.
-3 1
+
x
We substitute any number> 3.
3
- x
y
-2 O 2 x
y
O 1 x
y
x
x=-2¡¡ x=2¡¡
-1 1
O
y
x
x=-1¡¡
x=2
O
y
x
x=1
y=2
O 2
y
O 2 x
y
x
-1 3
O
y
O 2 x
y
x
-2
O
y
O x
y
-1 O 2 x
-3-3 4
x
y
O
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Y:\HAESE\CAM4037\CamAdd_02\053CamAdd_02.cdr Thursday, 3 April 2014 4:09:05 PM BRIAN