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Not sure what the problem might be with your installation.

It could help to know the operating system, the version of Sage, and the way it was it installed.

The output I get with Sage 9.5.beta4 built from source on macOS 10.14.6 is correct.

sage: f_x = (x**3 - x**2 + 3*x + 4) / (x**2 - 4*x + 3)
sage: plot(f_x, (x, 0, 4), detect_poles=True, ymin=-100, ymax=100)
Launched png viewer for Graphics object consisting of 3 graphics primitives

Sage plot for quotient of polynomials

Likewise on SageCell, currently running Sage 9.4.