AQA Further Paper 1 2020 June — Question 9 4 marks

Exam BoardAQA
ModuleFurther Paper 1 (Further Paper 1)
Year2020
SessionJune
Marks4
TopicPolynomial Division & Manipulation

9 The function f is defined by $$f ( x ) = \frac { x ( x + 3 ) } { x + 4 } \quad ( x \in \mathbb { R } , x \neq - 4 )$$ 9
  1. Find the interval ( \(a , b\) ) in which \(\mathrm { f } ( x )\) does not take any values.
    Fully justify your answer.
    9
  2. Find the coordinates of the two stationary points of the graph of \(y = \mathrm { f } ( x )\)
    9
  3. Show that the graph of \(y = \mathrm { f } ( x )\) has an oblique asymptote and find its equation.
    \section*{Question 9 continues on the next page} 9
  4. Sketch the graph of \(y = \mathrm { f } ( x )\) on the axes below.
    [0pt] [4 marks]
    \includegraphics[max width=\textwidth, alt={}, center]{44e22a98-6424-4fb1-8a37-c965773cb7b6-16_1100_1100_406_470}
    \includegraphics[max width=\textwidth, alt={}, center]{44e22a98-6424-4fb1-8a37-c965773cb7b6-17_2493_1732_214_139}
  5. Fird \(\begin{aligned} & \text { Do not write }
    & \text { outside the } \end{aligned}\)