Curve sketching strategy

We can use the same basic strategy to sketch any function:

1. Find the zeros, vertical asymptotes, and end behaviour of the function.
2. Take the first derivative and find the critical points.
3. Take the second derivative and find the key points.
4. Plot the y-intercept, zeros, critical points, key points.
5. Indicate any asymptotes with dashed lines.
6. Make three tables to indicate the signs of the value, slope, and concavity across the domain of the function.
7. Connect the points on the graph by drawing the curve one segment at a time (a segment being a region where none of the three quantities change).