Examples and practice
Graphing techniques
Back to lessonPractice section 1 · Questions 1–6
Find exact intercepts and verify the calculator window · Check exact intercepts of four rational curves · +4 more
Practice section 2 · Questions 7–12
Classify the two turning points exactly · Find exact input and output ranges · +4 more
Practice section 3 · Questions 13–18
Practise rational-curve features · Choose the correct branch of a modulus graph · +4 more
Practice section 4 · Questions 19–24
Use an asymptote family to find when no real roots occur · Link the discriminant interval to the missing horizontal levels · +4 more
- Use an asymptote family to find when no real roots occur
- Link the discriminant interval to the missing horizontal levels
- Recover the coefficients from a vertical and an oblique asymptote
- Use missing output levels and a circle comparison to count roots
- Respect the vertical-asymptote condition at the derivative boundary
- Differentiate a factored cubic and distinguish a repeated stationary point
Practice section 5 · Questions 25–30
Recast a quartic as a rational-curve intersection · Find absent output levels from a quadratic discriminant · +4 more
- Recast a quartic as a rational-curve intersection
- Find absent output levels from a quadratic discriminant
- Use a cosine amplitude bound that works for every phase and frequency
- Find a rational range and solve by adding a cosine sketch
- Check a cancellation exception before claiming a strict parameter range
- Connect a derivative discriminant to the missing range
Practice section 6 · Questions 31–32
Use completing the square before drawing a rational graph · Recover the curve from its range and count line intersections