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The graph will cross the y-axis once but will not cross or touch the x-axis.
In geometry, an asymptote is a line that approaches the axis of a graph but does not touch or intersect. The line will continue to get closer but will never actually touch the axis. The line is said to be "asymptotic" if this occurs.
The transverse axis is a connection on a hyperbola. It connects the focus, or center, of the hyperbola, and can connect two together.
On a graph it is where a point on a line/parabola/hyperbola/... Crosses the x-axis. And it can also be in parenthesis when written out. For example: (3,0)
The transverse axis is perpendicular to the conjugate axis.