Science:Math Exam Resources/Courses/MATH110/April 2011/Question 08 (f)/Solution 1

Using the information from parts (a) - (e), we draw the graph as follows.

First, we know that the function is undefined outside of $\displaystyle (-2,2)$ so we will shade out that portion of the graph.

Now we add in the two x-intercepts at $-{\sqrt {3}}$ and ${\sqrt {3}}$. We also include the information about the asymptotes - both $x=-2$ and $x=2$ were asymptotes, with the function going to $-\infty$.

Finally, incorporating the information from (d) and (e) about increase/decrease and concavity, and the maximum at x = 0, we connect the dots and finish the drawing.