The asymptotes are $x=\pm1$ and $y=2$. The curve intersects the horizontal asymptote at $x=7$. It intersects with the y-axis at $y=-5$. It has two turning points at $x \approx 0.1$ and $13.9$. Here is the sketch I made. However, plotting the graph with a graph plotter does not show the turning point on the right-most branch. Is this because I haven't 'zoomed enough', or is it something else?