Drawing Areas Between Curves: Tips & Tricks

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SUMMARY

This discussion focuses on the techniques for drawing areas between curves defined by inequalities, specifically the equations x - 2y² ≥ 0 and 1 - x - |y| ≥ 0. The first equation represents a hyperbola with a horizontal axis, while the second describes a "V" shaped line opening to the right. To accurately depict the regions defined by these inequalities, one must graph the corresponding equations and test points on either side of the curves to determine which regions satisfy the inequalities.

PREREQUISITES
  • Understanding of graphing inequalities in a Cartesian plane
  • Familiarity with hyperbolas and their properties
  • Knowledge of absolute value functions and their graphical representation
  • Ability to test points in inequalities to determine valid regions
NEXT STEPS
  • Study the properties of hyperbolas and their equations
  • Learn how to graph absolute value functions and their transformations
  • Practice solving and graphing systems of inequalities
  • Explore techniques for shading regions in multi-inequality graphs
USEFUL FOR

Students in mathematics, educators teaching algebra and calculus, and anyone interested in mastering the graphical representation of inequalities and areas between curves.

sobadin
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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 :smile:
 
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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].
 

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