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Finding Holes in Functions

Consider the following function:

Let's first find any vertical asymptotes by setting the denominator equal to zero and getting the result:

x - 2 = 0

x = 2

It appears we have a vertical asymptotes at x = 2.

But what does the actual graph look like of the function?

It appears it is roughly linear. How can that be? There doesn't appear to be an asymptote at x = 2...

What we have encountered is a hole in the equation, and it is a point where the function has no defined y value for a given x, yet the function appears continuous. This function is then defined as continuous and differentiable at all points except x = 2.