2023 May TZ2 P1 Q3

A function \(f\) is defined by \(f(x) = 1 - \frac{1}{x - 2}\), where \(x \in \mathbb{R}\), \(x \neq 2\).

1. The graph of \(y = f(x)\) has a vertical asymptote and a horizontal asymptote.

   Write down the equation of

   1. the vertical asymptote;

   2. the horizontal asymptote.

      [2]

2. Find the coordinates of the point where the graph of \(y = f(x)\) intersects

   1. the \(y\)-axis;

   2. the \(x\)-axis.

      [2]

3. On the following set of axes, sketch the graph of \(y = f (x)\), showing all the features found in parts (a) and (b).

   [1]