Science:Math Exam Resources/Courses/MATH110/April 2013/Question 02 (b)/Solution 1

See the second hint for how each limit translates into a feature of the graph.

1. Your graph can do whatever it wants to the left of x = -1, so long as it approaches the point (-1,0). The simplest (yet somewhat boring) way to achieve this is by setting the function to 0 for x < -1.
2. Between x = -1 and x = 1 the function has to fall from $\infty$ to $-\infty$.
3. To the right of x = 1 the function has to come back from $-\infty$ and then can do whatever you want it to do.

There is a lot of freedom in how your graph may look, but as long as you follow the key points above your graph will be correct. Below is our example (the purple lines represent asymptotes):