\(x^{3} - 17 x^{2} + 42 x = 3 x^{2} + 6 x\)
\(x^{3} - 20 x^{2} + 36 x = 0\)
\(x (x^{2} - 20 x + 36) = 0\)

\(x (x - 2) (x - 18) = 0\)
\(x = 0 ∨ x = 2 ∨ x = 18\)

\(f(x) > g(x)\) geeft \(0 < x < 2 ∨ x > 18 \text{.}\)

\(f(1) = -1 \text{.}\)

\(-2 x + 6 ≥ 0\)
\(-2 x ≥ -6\)
\(x ≤ 3\)
Dus het randpunt is \((3 , 5) \text{.}\)

\(x > 1\) geeft \(-1 < f(x) ≤ 5 \text{.}\)

\(-3 - 4 \sqrt{-6 x + 6} = -27\)
\(-4 \sqrt{-6 x + 6} = -24\)
\(\sqrt{-6 x + 6} = 6\)
\(-6 x + 6 = 36\)
\(-6 x = 30\)
\(x = -5 \text{.}\)

\(-6 x + 6 ≥ 0\)
\(-6 x ≥ -6\)
\(x ≤ 1\)
Dus het randpunt is \((1 , -3) \text{.}\)

\(f(x) > -27\) geeft \(-5 < x ≤ 1 \text{.}\)

\(f(x) = 9\)
\(3 ⋅ {}^{2}\!\log(-x + 6) + 6 = 9\)
\(3 ⋅ {}^{2}\!\log(-x + 6) = 3\)
\({}^{2}\!\log(-x + 6) = 1\)
\(-x + 6 = 2^{1} = 2\)
\(-x = -4\)
\(x = 4\)

Bereking van het domein geeft
\(-x + 6 > 0\)
\(-x > -6\)
\(x < 6\)
Dus de verticale asymptoot is de lijn \(x = 6 \text{.}\)

\(f(x) < 9\) geeft \(4 < x < 6 \text{.}\)