1. 1
   The graph of $y = f(x)$ has a single marked point at $(2, 5)$.

   (a)

   What are the coordinates of the corresponding point on the graph of $y = f(x) + 4$?

   [1 mark]

   • A$(6, 5)$
   • B$(2, 9)$
   • C$(2, 1)$
   • D$(-2, 5)$

   (b)

   What are the coordinates of the corresponding point on the graph of $y = f(x - 3)$?

   [1 mark]

   • A$(-1, 5)$
   • B$(2, 8)$
   • C$(5, 5)$
   • D$(2, 2)$

   (c)

   What are the coordinates of the corresponding point on the graph of $y = -f(x)$?

   [1 mark]

   • A$(-2, -5)$
   • B$(-2, 5)$
   • C$(2, 5)$
   • D$(2, -5)$

   Total for question 1: 3 marks

2. 2
   The graph of $y = g(x)$ has a maximum turning point at $(-1, 6)$.

   (a)

   Find the coordinates of the turning point of $y = g(x) - 5$, and state whether it is a maximum or a minimum.

   [2 marks]

   (b)

   Explain why the graph of $y = g(-x)$ has a maximum turning point at $(1, 6)$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The graph of $y = \sin x$ is transformed in two different ways: transformation P gives $y = \sin x + 2$, and transformation Q gives $y = \sin(x + 90)$.

   (a)

   Describe fully transformation P, and state the maximum and minimum values of the transformed graph.

   [3 marks]

   (b)

   Describe fully transformation Q, and state the value of $y$ when $x = 0$ on the transformed graph.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A student is investigating the graph of $y = f(x) = x^2 - 6x + 8$, which can be written in completed square form as $f(x) = (x-3)^2 - 1$.

   (a)

   By completing the square, find the coordinates of the turning point of $y = f(x)$, and hence state the coordinates of the turning point of $y = f(x) + 5$.

   [4 marks]

   (b)

   State the coordinates of the turning point of $y = f(x - 2)$, and explain how you obtained your answer using the rule for horizontal translations.

   [4 marks]

   (c)

   The graph of $y = f(x)$ is reflected in the $x$-axis to give $y = -f(x)$, then translated $3$ units in the positive $x$-direction. Find the coordinates of the turning point of the final graph, showing each transformation step and stating whether it is a maximum or minimum.

   [5 marks]

   Total for question 4: 13 marks

End of questions