Voor welke van de volgende functies zijn   x = 2   én   y = − 3   asymptoten ?
A.  \(\large\boldsymbol{f_A(x)=\frac{x^2\,-\,7}{3x\,-\,6}}\)
B.  \(\large\boldsymbol{f_B(x)=\frac{8x\,-\,3x^2}{x^2\,-\,2x} }\)
C.  \(\large\boldsymbol{f_C(x)=\frac{3x}{x\,-\,2} }\)
D.  \(\large\boldsymbol{f_D(x)=\frac{2x}{x\,+\,3} }\)
E.  \(\large\boldsymbol{f_E(x)=\frac{x\,-\,5}{x\,-\,2}}\)
A    B    C    D    E

[ 5-5956 - op net sinds 2.1.13-(E)-4.11.2024 ]

Translation in   E N G L I S H

Which function has asymptotes of  
x = 2   and   y = − 3 ? 		A.   \(\boldsymbol{f_A(x)=\frac{x^2\,-\,7}{3x\,-\,6}}\)
B.   \(\boldsymbol{f_B(x)=\frac{8x\,-\,3x^2}{x^2\,-\,2x} }\)
C.   \(\boldsymbol{f_C(x)=\frac{3x}{x\,-\,2} }\)
D.   \(\boldsymbol{f_D(x)=\frac{2x}{x\,+\,3} }\)
E.   \(\boldsymbol{f_E(x)=\frac{x\,-\,5}{x\,-\,2}}\)

Oplossing - Solution

A → verticale asymptoot x = 2   geen horizontale asymptoot
B → \(f_B(x)=\frac {8x-3x^2} {x^2-2x}=\frac{x(8-3x)}{x(x-2}=\frac{8-3x}{x-2} \)   voor x ≠ 0
    verticale asymptoot x = 2   horizontale asymptoot y = −3
C → verticale asymptoot  x = 2   horizontale asymptoot  y = 3
D → verticale asymptoot  x = −3 horizontale asymptoot  y = 2
E → verticale asymptoot  x = 2   horizontale asymptoot  y = 1
gricha