Question 1

1. [Maximum mark: 5]

The function $f$ is defined by $f(x) = \frac{3x - 2}{2x + 1}$ for $x \in \mathbb{R}, x \neq -\frac{1}{2}$.

The following diagram shows part of the graph of $y = f(x)$.

(a) Write down the value of $f(0)$. [1]

(b) Write down the equation of the horizontal asymptote. [1]

The function $g$ is defined by $g(x) = -f(x)$ for $x \geq 0$.

(c) Find the range of $g$. [3]