H2 Maths 1.2 - Sketch a Rational Function with Stationary Points

What you will learn

• Sketch y = (x^2 - x + 4) / (x - 2); long division gives y = x + 1 + 6 / (x - 2).
• Asymptotes: vertical x = 2, oblique y = x + 1; no x-intercepts (discriminant -15 < 0), y-intercept (0, -2).
• Stationary points from dy/dx = 1 - 6 / (x - 2)^2 = 0 at x = 2 plus or minus sqrt(6).