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The "vertical line test" will tell you if it is a function or not. The graph is not a function if it is possible to draw a vertical line through two points.
Yes, x = -3 would represent a vertical line at abscissa -3, parallel to the y-axis.
A graph is a function if any vertical line intersects it at most once.
When you graph a tangent function, the asymptotes represent x values 90 and 270.
Yes the graph of a function can be a vertical or a horizontal line