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When you graph a tangent function, the asymptotes represent x values 90 and 270.
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.
a) A circle is not the graph of a function. b) A circle is not linear.
A cartesian graph is a graph in which y is some function of x. This is the 'normal' type in which you can give an x and y coordinate. Other types include polar in which modulus is a function of argument, but there are loads of varieties and forms.
The coordinates of the points on the curve represent solutions of the equation.