The line x = 3 is a vertical asymptote to the graph of f. Find the value of c.

Write down the equation of the horizontal asymptote to the graph of f.

The line y = k, where $k \in \mathbb{R}$ intersects the graph of $\left| {f\left( x \right)} \right|$ at exactly one point. Find the possible values of k.

valid approach       (M1)
eg  $cx + 6 = 0,\,\, - \frac{6}{c} = 3$

c = −2      A1 N2

[2 marks]

valid approach (M1)
eg  $\mathop {{\text{lim}}\,f}\limits_{x \to \infty } \left( x \right),\,\,y = \frac{8}{c}$

y = −4 (must be an equation)      A1 N2

[2 marks]

valid approach to analyze modulus function      (M1)
eg   sketch, horizontal asymptote at y = 4, y = 0

k = 4, k = 0     A2 N3

[3 marks]