Help !! How do I graph and solve rational functions? Ex: f(x) =-1/x-3 +1

Graph:  f(x)  =  -1/(x - 3) + 1

 

This becomes a hyperbola with asymptotes at:  x = 3  and  y = 1.

Since the coefficient of the x-term is negative, it will graph in the upper-left and lower-right portions of the plane separated by the asymptotes.

 

As the values for x get very large, the y-values approach 1 from below.

As the values for x get very small (large negative), the y-values approach 1 from above.

 

As the values for x approach 3 from the left, the values for y go to positive infinity.

As the values for x approach 3 from the right, the values for y go to negative infinity.