1. Find all the horizontal asymptotes, if any, of the function
\(f(x) = \frac{3 - 4x}{2x + \sqrt{16x^2 - x - 5}}\)
2. Given the function
\(f(x) = \begin{cases} (kx)^2 - 3kx + k, & x \neq -2 \\ 9 - 2k, & x = -2 \end{cases}\)
use the definition of continuity to determine all values of the constant \(k\) for which \(f(x)\) is
continuous at \(x = -2\).
3. Given the function
\(f(x) = \begin{cases} \frac{x^2 + 5x + 4}{x^2 + 3x - 4}, & \text{for } x \le 0 \\\ x - 1, & \text{for } 0 < x \le 2 \\\ \frac{x^2 - 7x + 10}{x^2 - 10x + 25}, & \text{for } x > 2 \end{cases}\)
use the definition of continuity to investigate the continuity of \(f(x)\) at each of the following.
Classify any discontinuities as removable or non-removable.
(a) \(x = 0\)
(b) \(x = 2\)
(c) any other points where \(f(x)\) is discontinuous
