What is the shape of the graph of #|x|+|y|<1#?
2 Answers
The easiest thing is to just show you the graph
Explanation:
It is a diamond-shaped graph centred at the origin, with all 4 corners on the axes, 1 unit from the origin. The lines are dotted (to indicate "not equal to"), and the diamond is filled (to indicate "less than").
Explanation:
We're looking for all the points
Picture a taxi, picking someone up at the origin
It's easy; the taxi must go at least 0.6 units right, and 0.3 units up, for a total of 0.9 units of travel. It doesn't matter if the driver moves in a kind of "staircase" manner, they will still reach their destination after a total of 0.6 units right and 0.3 up. This means the point
And it doesn't matter if the passenger wants to go to the left or down, either; what we're looking for is to keep the total distance from the origin less than 1, so all we need to do is find all points that are within a taxicab distance of 1 from the origin.
Here is a graph of