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Print value of vertical & horizontal asymptote?

By default the program draws a blue line displaying the vertical asymptote of a function, which is very helpful. If I could get it to display a line through the horizontal asymptote, & print their value, if would be very helpful.

I attempted the following to get the vertical asymptote & had no luck at all:

ans = solve( 7/(x-3) == 0, x)
v0 = ans[0].rhs()

Error message:

Traceback (click to the left of this block for traceback)
IndexError: list index out of range