Analyzing function behavior

1003259608

Level: 
C
Determine the values of \( a \), \( b \) (\( a \), \( b\in\mathbb{R} \)) such that the line \( y=2x+\frac13 \) is an asymptote of the graph of the function \( f(x)=\frac x{ax-1}+bx \).
\( a=3 \), \( b=2 \)
\( a=\frac12 \), \( b=3 \)
\( a=2 \), \( b=\frac13 \)
\( a=\frac12 \), \( b=\frac13 \)
\( a=\frac13 \), \( b=2 \)

1003259609

Level: 
C
Determine the values of \( a \), \( b \) (\( a \), \( b\in\mathbb{R} \)) such that the line \( y=0 \) is an asymptote of the graph of the function \( f(x)=\frac x{ax-1}+bx \).
there are no such \( a \), \( b \)
\( a\in\mathbb{R}\setminus\{1\} \), \( b=0 \)
\( a=0 \), \( b=0 \)
\( a\in\mathbb{R} \), \( b=0 \)

1003259610

Level: 
C
Let there be a function \( f(x)=\frac{ax^2}{x-b} \), \( a \), \( b\in\mathbb{R} \). Determine the values of \( a \), \( b \), such that the line \( y=3x+2 \) is an asymptote of the graph of the function \( f \).
\( a=3 \), \( b=\frac23 \)
\( a=3 \), \( b=\frac43 \)
\( a=3 \), \( b=2 \)
\( a=2 \), \( b=\frac32 \)
there are no such \( a \), \( b \)