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Vertical line test for function of two variables

Raj Kumar
16/08/2018 0 0

Vertical line test says that any line that is parallel to z-axis any line of form x=x0 and y=y0

intersect the graph z=f(x,y) of function at most one point

.because there is a point of intersection if and only if (x0, y0) is in the domain of the function

Otherwise, there is no existence of a point of intersection

As we Know from the definition of the graph of a function of two variables to each point (x,y) in the domain there

corresponds a point (x,y,z) on the surface and conversely to each position on the surface there corresponds a spot in the domain

hence a vertical line can intersect the graph at most once.

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