Jambmaths question:
The diagram above is the graph of the function f(x). Determine the range of values of x for which $f(x)\le 0$
Option A:
$0\le x\le 2$
Option B:
$x\le 2$
Option C:
$x\le -2,\text{ }0\le x\le 2$
Option D:
$-2\le x\le 0,\text{ }x\ge 2$
Jamb Maths Solution:
From the graph above we
$x(x-2)(x+2)\le 0$
We have to draw the range table to be able to know the actual range
|
|
$x\le -2$ |
$-2\le x\le 0$ |
$0\le x\le 2$ |
$x\ge 2$ |
|
x |
– |
– |
+ |
+ |
|
(x – 2) |
– |
– |
– |
+ |
|
(x +2) |
– |
+ |
+ |
+ |
|
x(x – 2) (x +2) |
– |
+ |
– |
+ |
So, from the range table drawn above, we will consider the negative (–), since 
$f(x)\le 0$ will hold true when $x\le -2$ and $0\le x\le 2$
.So option C is the correct option
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