Question 10.6.1: Sketching a Surface Draw a graph of the surface z = y² in R³...
Sketching a Surface
Draw a graph of the surface z=y^2 \text { in } R ^3.
Since there are no x’s in the equation, the trace of the graph in the plane x=k is the same for every k. This is then a cylinder whose trace in every plane parallel to the y z \text {-plane is the parabola } z=y^2 \text {. } To draw this, we first draw the trace in the y z \text {-plane } and then make several copies of the trace, locating the vertices at various points along the x-axis. Finally, we connect the traces with lines parallel to the x \text {-axis } to give the drawing its three-dimensional look. (See Figure 10.53a.) A computer-generated wireframe graph of the same surface is seen in Figure 10.53b. Notice that the wireframe consists of numerous traces for fixed values of x or y.
