Worksheets · Higher

Translations and reflections of function graphs

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Non-calculator · 4 marks

   The curve $y = f(x)$ has a turning point at $(2, -3)$.

   (a) Write down the coordinates of the turning point of $y = f(x) + 4$. (1)

   (b) Write down the coordinates of the turning point of $y = f(x - 3)$. (1)

   (c) Write down the coordinates of the turning point of $y = -f(x)$. (1)

   (d) Write down the coordinates of the turning point of $y = f(-x)$. (1)
2. Question 2Calculator · 3 marks

   (a) f(x) = $x^{2}$ $-$ 6x + 5. Find the coordinates of the maximum point on the graph y = $-f$(x $-$ 2) + 7. (3)
3. Question 3Non-calculator · 3 marks

   The curve y = f(x) passes through A(-2, 0), B(1, 4) and C(3, 0).

   (a) Write down the coordinates of the image of B on the curve y = f(x + 2). (1)

   (b) Write down the coordinates of the image of B on the curve y = -f(x). (1)

   (c) Write down the solutions of f(x - 1) = 0. (1)