Exploring Three-Dimensional Cartesian Coordinate Systems and Graphing Multivariable Functions
Dive into the fundamentals of three-dimensional Cartesian coordinate systems, where the x-axis extends from front to back, the y-axis from left to right, and the z-axis from top to bottom. Learn how these axes divide space into 8 octants, each represented by different combinations of positive and negative coordinates. Discover how to plot points and graph multivariable functions in 3D space, honing your skills through examples and practice assignments to solidify your understanding of the concepts.
Exploring Three-Dimensional Cartesian Coordinate Systems and Graphing Multivariable Functions
E N D
Presentation Transcript
Section 10-4 Graphing Multivariable functions
Z X Y Three Dimensional Cartesian Coordinate System
Coordinate Axis The x-axis appears to go from front to back the y-axis from left to right the z-axis from top to bottom The positive x direction is from the origin forward The positive y direction is from the origin right The positive z direction is from the origin up
Octants The three axis divide the space into 8 octants. Four above the xy plane and four below the xy plane
Octants I. (x, y, z) II. (-x, y z) III. (-x, -y, z) IV. (x, -y, z) V. (x, y -z) VI. (-x, y, -z) VII. (-x, -y, -z) VIII. (x, -y, -z)
Z X Y Plot the points A( 2, 3, 5 ) B( 0, 5, 2 ) C( 2, -2, -4 )
z y x 3. Graph the plane y = 5
z y x 4.
z y x 5.
Assignment: Practice 10-4
