4 8 points LarCalc11 131041 My Notes Consider the following

4. -/8 points LarCalc11 13.1.041 My Notes Consider the following function. rx, y) = e-x Describe the surface given by the function Because the variable y is missing, the surface is a plane with rulings parallel to the x-axisThe generating curve is z = e-x. The domain is the entire xy-plane and the range is z > Sketch the surface given by the function. -2 8 -Q 0 Need Help? Read It Talk to a Tutor

Solution

Since, given function is of two variables, x and y. Therefore, we will plot z = f(x,y, i.e. the z-value at (x, y).

Further, as z is independent of y, because z = e^-x, therefore for any value of y, the graph will be the curve z = e^-x, (i.e. the same curve in xz-plane).

Therefore, draw the graph z = e^-x in xz-plane, then sweep the graph for all y, which will define the desired surface.