Curve sketching strategy
We can use the same basic strategy to sketch any function:
- Find the zeros, vertical asymptotes, and end behaviour of the function.
- Take the first derivative and find the critical points.
- Take the second derivative and find the key points.
- Plot the y-intercept, zeros, critical points, key points.
- Indicate any asymptotes with dashed lines.
- Make three tables to indicate the signs of the value, slope, and concavity across the domain of the function.
- 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).