Qualititative description of graphs

When characterising a graph look for asymptotic behaviour - as x goes to -∞ and +∞. Also look for points where y goes to +/-∞.

If you have to sketch 1/f, then if f goes to ∞ then 1/f goes to 0. Whether it crosses 0 or just touches depends on whether the sign of f changes or stays the same on each side of the ∞.

If you are sketching 1/f also pay attention to where f crosses or touches 0, in which case 1/f goes to ∞. The same considerations apply as above.

If f is -1 or +1 then 1/f is of course the same, so look out for those points as well - these are points where the graph of 1/f will cross the graph of f.