Rational Function Asymptotes

2 The equation of a curve is \(y = \frac { x ^ { 2 } - 3 } { x - 1 }\).

1. Find the equations of the asymptotes of the curve.
2. Write down the coordinates of the points where the curve cuts the axes.
3. Show that the curve has no stationary points.
4. Sketch the curve and the asymptotes.

6 The curve \(C\) has equation $$y = \frac { x ^ { 2 } + b } { x + b }$$ where \(b\) is a positive constant.

1. Find the equations of the asymptotes of \(C\).
2. Show that \(C\) does not intersect the \(x\)-axis.
3. Justifying your answer, find the number of stationary points on \(C\).
4. Sketch C. Your sketch should indicate the coordinates of any points of intersection with the \(y\)-axis. You do not need to find the coordinates of any stationary points.

4 The curve \(C\) has equation $$y = \frac { x ^ { 2 } + 7 x + 6 } { x - 2 }$$

1. Find the coordinates of the points of intersection of \(C\) with the axes.
2. Find the equation of each of the asymptotes of \(C\).
3. Sketch C.

Which of the straight lines given below is an asymptote to the curve $$y = \frac{ax^2}{x-1}$$ where \(a\) is a non-zero constant? Circle your answer. [1 mark] \(y = ax + a\) \quad\quad \(y = ax\) \quad\quad \(y = ax - a\) \quad\quad \(y = a\)