Given the function:
the vertical asymptote;
the horizontal asymptote;
the intersection point with the -as if it exists;
the intersection point with the -as if it exists.
Based on these results sketch the result in the figure.
The line seems to be an asymptote. However, when we substitute this value in the formula we get . That the numerator yields for means that the numerator contains the factor . Indeed, the numerator can be factorized: . Now the function can be rewritten:
We do not need to do complicated calculations any more. There also no asymptotes. The graph of the function is equal to the graph of , excluded the point . The graph approaches if approaches The graph in the figure is valid, exluded the point .