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Date May 2018 Marks available 3 Reference code 18M.2.sl.TZ2.7
Level SL only Paper 2 Time zone TZ2
Command term Find Question number 7 Adapted from N/A

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.

[2]
a.

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

[2]
b.

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.

[3]
c.

Markscheme

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

c = −2      A1 N2

[2 marks]

a.

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]

b.

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

k = 4, k = 0     A2 N3

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 2 - Functions and equations » 2.5 » The reciprocal function \(x \mapsto \frac{1}{x}\) , \(x \ne 0\) : its graph and self-inverse nature.

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