In this last section we have to discuss graphing rational functions.  It's is possibly best to begin along a rather simple one that we can do with no all that much knowledge on how these work.

Let's sketch the graph of f ( x ) = 1/x .  Firstly, as this is a rational function we will have to be careful with division by zero issues.  Thus, we can see from this equation which we'll ought to avoid x = 0 as that will give division by zero.

 Now, let's just plug in some of values of x and see what we obtain.

Thus, as x get large (positively and negatively) the function keeps the sign of x & gets smaller & smaller.  Similarly as we approach x = 0 the function again keeps the similar sign as x however start getting quite large.  Following is a sketch of this graph.

Firstly, notice that the graph is into two pieces.  Almost all of the rational functions will have graphs in multiple pieces like this.

Next, notice that this graph does not contain any intercepts of any kind.  That's simple sufficient to check for ourselves.