Question
Let \(f(x) = p + \frac{9}{{x – q}}\), for \(x \ne q\). The line \(x = 3\) is a vertical asymptote to the graph of \(f\).
Write down the value of \(q\).
The graph of \(f\) has a \(y\)-intercept at \((0,{\text{ }}4)\).
Find the value of \(p\).
The graph of \(f\) has a \(y\)-intercept at \((0,{\text{ }}4)\).
Write down the equation of the horizontal asymptote of the graph of \(f\).
Answer/Explanation
Markscheme
\(q = 3\) A1 N1
[1 mark]
correct expression for \(f(0)\) (A1)
eg\(\;\;\;p + \frac{9}{{0 – 3}},{\text{ }}4 = p + \frac{9}{{ – q}}\)
recognizing that \(f(0) = 4\;\;\;\)(may be seen in equation) (M1)
correct working (A1)
eg\(\;\;\;4 = p – 3\)
\(p = 7\) A1 N3
[3 marks]
\(y = 7\;\;\;\)(must be an equation, do not accept \(p = 7\) A1 N1
[1 mark]
Total [6 marks]