You can have asymptotes in the x or y direction.
The function y = e-x goes to zero as x goes to infinity. So the root (when x = 0) is only "reached" asymptotically.
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Yes and they will be of equal value
if it touches at three points it is a straight line. Since it is also an asymptote, it will be a straight horizontal line (zero slope)
Set 'x' equal to zero, and solve the remaining equation for 'y'.
If the discriminant of the quadratic equation is zero then it will have 2 equal roots. If the discriminant of the quadratic equation is greater than zero then it will have 2 different roots. If the discriminant of the quadratic equation is less than zero then it will have no roots.