How Do You Sketch the Graph of f(x,y) = 1 - y^2?

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SUMMARY

The function f(x,y) = 1 - y^2 represents a parabolic cylinder in three-dimensional space. Its cross-section in the yz-plane is a parabola defined by z = 1 - y^2, which opens downward. The graph extends infinitely along the x-axis, creating a cylindrical shape. This visualization is crucial for understanding the behavior of the function in a three-dimensional context.

PREREQUISITES
  • Understanding of three-dimensional graphing concepts
  • Familiarity with parabolic equations
  • Knowledge of coordinate systems (Cartesian coordinates)
  • Basic skills in sketching mathematical functions
NEXT STEPS
  • Research techniques for graphing three-dimensional functions
  • Learn about parabolic cylinders and their properties
  • Explore software tools for 3D graphing, such as GeoGebra
  • Study the implications of cross-sections in multi-variable functions
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Students in mathematics, educators teaching graphing techniques, and anyone interested in visualizing multi-variable functions in three dimensions.

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Homework Statement



Sketch the graph of the function f(x,y) = 1 - y^2

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The Attempt at a Solution



see pic
 

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That's a two dimensional graph- it looks like x= 1- y2. But you are asked to graph z= f(x,y)= 1- y2 in 3 dimensions. The graph is a parabolic cylinder. It's cross section is the parabola z= 1- y2 in the yz-plane but it extends infinitely along the x-axis.
 
ahh brain fart


hows the new pic
 

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