# Thread: Assistance with sketching relations

1. ## Assistance with sketching relations

The question:

Sketch the set of points (x, y) which satisfy the following relations:

0 <= y <= 2x and 0 <= x <=2

I have no idea where to start. Is there a way to simultaneously equate them? Is the process supposed to be intuitive? I can't get my head around it.

Any guidance would be greatly appreciated.

2. Originally Posted by Glitch
The question:

Sketch the set of points (x, y) which satisfy the following relations:

0 <= y <= 2x and 0 <= x <=2

I have no idea where to start. Is there a way to simultaneously equate them? Is the process supposed to be intuitive? I can't get my head around it.

Any guidance would be greatly appreciated.
Hi Glitch,

If x (domain) is between 0 and 2, inclusive,
then y (range) is between 0 and 4, inclusive.

Sketch 0 to 2 on the x-axis, and 0 to 4 on the y-axis.

Complete the rectangle with corners at (0, 0), (0, 4), (2, 4), (2, 0).

All the points inside the rectangle, including the corners and edges, satisfy the given conditions.

So when determining the range, how did you know it was between 0 and 4 inclusive? Did you substitute the upper bound of x?

4. Originally Posted by Glitch

So when determining the range, how did you know it was between 0 and 4 inclusive? Did you substitute the upper bound of x?
Yes, I did.

5. Hello, Glitch!

Sketch the set of points (x, y) which satisfy: . $\begin{array}{ccccc}0 & \leq & y & \le &2x \\ 0 & \le &x & \le &2 \end{array}$

$0 \:\le\: y \:\le\:2x$ means $y$ is between the lines: . $\begin{Bmatrix}y &=& 2x \\ y &=& 0 \end{Bmatrix}$

The graph looks like this:

Code:
      |
|               *:::::
|             *::::::
|           *:::::::::
|         *::::::::::
|       *:::::::::::::
|     *::::::::::::::
|   *:::::::::::::::::
| *::::::::::::::::::::
- - * - - - - - - - - - - - -
0

$0\:\le\: x \:\le\:2$ means $x$ is between the lines: . $\begin{Bmatrix}x &=&2 \\ x &=& 0\end{Bmatrix}$

Code:
      |
|:::::::::|
|:::::::::|
|:::::::::|
|:::::::::|
|:::::::::|
|:::::::::|
- - * - - - - + - - - - - - -
0         2

The region satisfying both inequalities is the area shaded twice.

Code:
      |
|         *
|       *:|
|     *:::|
|   *:::::|
| *:::::::|
- - * - - - - + - - -
0         2