Cannot exist. And a vertical graph is simply a vertical graph!
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Yes the graph of a function can be a vertical or a horizontal line
The line x = 4 is a verticle line because, in a standard x-y graph, where x increases to the right and y increases upwards, the graph x = 4 is all points y, where x is 4. That is a verticle line, with infinite slope.
So this would be a verticle line which passes through the point at -3.
Verticle angles are angles opposite each other when two lines cross
Not sure what non-verticle means, but a rational function can have up to 2 non-vertical asymptotes,