Download IITian Academy App for accessing Online Mock Tests and More..
Question
Let \(f\left( x \right) = \frac{{8x – 5}}{{cx + 6}}\) for \(x \ne – \frac{6}{c},\,\,c \ne 0\).
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.
Answer/Explanation
Markscheme
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]