1.26: Past-paper question 3

Curve $\displaystyle S$ has equation $\displaystyle y = 2 - \frac{5}{2x+1}$ where $\displaystyle x \neq -\frac{1}{2}$

(a) Write down an equation of the asymptote to $\displaystyle S$ that is parallel to

(i) the $\displaystyle y$-axis

(ii) the $\displaystyle x$-axis

(b) Find the coordinates of the point where $\displaystyle S$ crosses

(i) the $\displaystyle y$-axis

(ii) the $\displaystyle x$-axis

(c) Using the axes on the page opposite, sketch $\displaystyle S$, showing clearly the asymptotes and the coordinates of the points where $\displaystyle S$ crosses the coordinate axes.