1.3: Reciprocal curves and asymptotes and curve intersections

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

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

(i) the $y$-axis

(ii) the $x$-axis

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

(i) the $y$-axis

(ii) the $x$-axis

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