2026 MAY TZA P1 Q7

Consider the function \(f(x) = \frac{2x - 3}{3 - x}\), \(x \in \mathbb{R}\), \(x \neq 3\).
The graph of \(f\) and its asymptotes are shown in the following diagram

1. Find the equation of

   [3]

   1. the vertical asymptote;

   2. the horizontal asymptote.

2. Find the coordinates of the points where the graph of \(f\) intersects the coordinates axes.

   [4]

Consider the function \(g(x) = x + 4\), \(x \in \mathbb{R}\).

3. [5]

   1. Describe the transformation that transforms the graph of \(y = f(x)\) to the graph of \(y = (g \circ f)(x)\).

   2. Hence, find the range of \(g \circ f\).