Drawing Areas Between Curves: Tips & Tricks

In summary, the conversation is about drawing diagrams for a topic that involves regions defined by inequalities. The person asking the question is struggling with drawing the diagrams and is confused about how to approach it. The solution is to draw graphs of the corresponding equations and use points on each side of the curve to determine the direction of the inequalities.
  • #1
sobadin
1
0
I know its a really dumb question and if i reached this far in math i should know but..how do you draw the diagrams for this topic? Like they give you a region in a plane defined by some kind of inequalities such as (x-2y^2 greater than or equal to 0), (1-x- IyI greater than or equal to 0) and tell you draw it...and I am just spaced out drawing circles all over my paper at this point...THE BEGINNING :rofl:
 
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  • #2
Do you mean [itex]x- 2y^2\ge 0[/itex] and [itex]1- x- |y|\ge 0[/itex]?

Draw graphs of the corresponding equations. [itex]x- 2y^2= 0[/itex] is the same as [itex]x= 2y^2[/itex], a hyperbola with horizontal axis. 1- x- |y|= 0 is the same as x= 1-|y|, a "broken" line or a "V" opening to the right. Then take one point on each side of the curve to decide which side is "[itex]\ge[/itex]" and which is "[itex]\le[/itex].
 

1. What is the purpose of drawing areas between curves?

The purpose of drawing areas between curves is to visually represent the relationship between two sets of data. It allows for a comparison of the values and can help identify patterns or differences between the two sets of data.

2. How do I determine which curve goes on top?

The curve that represents the larger values should go on top. This will make the area between the curves easier to interpret, as it will be clear which set of data has higher values. Additionally, it is important to consistently place the same curve on top when comparing multiple sets of data.

3. What is the best way to shade the area between curves?

The most common way to shade the area between curves is to use a solid or transparent color. This will make the area stand out and be easily distinguishable from the rest of the graph. However, you can also use patterns or textures for a more unique visual effect.

4. How can I label the shaded area between curves?

You can label the shaded area between curves by adding a legend to your graph. This will allow you to clearly identify which curve represents which set of data and what the shaded area represents. You can also add text directly onto the shaded area if you prefer.

5. Are there any other tips or tricks for drawing areas between curves?

One helpful tip is to make sure your curves are smooth and do not have any sharp turns or spikes. This will make the shaded area more accurate and easier to interpret. Additionally, you can experiment with different colors and shading techniques to make your graph more visually appealing and easier to understand.

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