In general, the graph of an inequality is a shaded area.
Consider the graph
y=∣x∣y=∣x∣ size 12{y= lline x rline } {} shown above. Every point on that V-shape has the property that its yy size 12{y} {}-value is the absolute value of its xx size 12{x} {}-value. For instance, the point
(
−
3,3
)
(
−
3,3
)
size 12{ \( - 3,3 \) } {}
is on the graph because 3 is the absolute value of –3.
The inequality
y
<
|
x
|
y
<
|
x
|
means the yy size 12{y} {}-value is less than the absolute value of the xx size 12{x} {}-value. This will occur anywhere underneath the above graph. For instance, the point
(
−
3,1
)
(
−
3,1
)
meets this criterion; the point
(
−
3,4
)
(
−
3,4
)
does not. If you think about it, you should be able to convince yourself that all points below the above graph fit this criterion.
The dotted line indicates that the graph
y=∣x∣y=∣x∣ size 12{y= lline x rline } {} is not actually a part of our set. If we were graphing
y≤∣x∣y≤∣x∣ size 12{y <= lline x rline } {} the line would be complete, indicating that those points would be part of the set.
"DAISY and BRF versions of this collection are available."