Name: ___________________________

GCSE (1 – 9)

Transforming Graphs

Instructions

• Use black ink or ball-point pen.

• Answer all questions.
• Answer the questions in the spaces provided
– there may be more space than you need.
• Diagrams are NOT accurately drawn, unless otherwise indicated.
• You must show all your working out.

Information

• The marks for each question are shown in brackets

– use this as a guide as to how much time to spend on each question.

Advice

• Read each question carefully before you start to answer it.

• Keep an eye on the time.
• Try to answer every question.
• Check your answers if you have time at the end

mathsgenie.co.uk
1 The graph of y = f(x) is shown below.

(1, 4)
y = f(x)

O x

The coordinates of the maximum point of this curve are (1, 4).

Write down the coordinates of the maximum point of the curve with equation

(a) y = f(x + 3)

…..........................
(1)
(b) y = –f(x)

…..........................
(1)
(c) y = f(x) – 3

…..........................
(1)

(d) y = f(–x)

…..........................
(1)

(Total for question 1 is 4 marks)

2 The graph of y = f(x) is shown below.

y = f(x)

O x

(2, –3)

The coordinates of the minimum point of this curve are (2, –3).

Write down the coordinates of the minimum point of the curve with equation

(a) y = f(x + 2)

…..........................
(1)
(b) y = –f(x)

…..........................
(1)
(c) y = f(x) + 2

…..........................
(1)

(d) y = f(–x)

…..........................
(1)

(Total for question 2 is 4 marks)

3 The graph of y = f(x) is shown below.

(–2, 1)
y = f(x)

O x

The coordinates of the maximum point of this curve are (–2, 1).

Write down the coordinates of the maximum point of the curve with equation

(a) y = f(x – 3)

…..........................
(1)
(b) y = f(–x)

…..........................
(1)
(c) y = –f(x + 2)

…..........................
(1)

(d) y = f(–x) – 1

…..........................
(1)

(Total for question 3 is 4 marks)

4 The graph of y = f(x) is shown on both grids below.

y
5

-4 -3 -2 -1 O 1 2 3 4
-1
x
-2

-3
-4
-5

(a) On the grid above, sketch the graph of y = –f(x).

(2)
y
5

-4 -3 -2 -1 O 1 2 3 4
-1
x
-2

-3
-4
-5

(b) On the grid above, sketch the graph of y = f(x + 2)

(2)

(Total for question 4 is 4 marks)

5 The graph of y = f(x) is shown on both grids below.

y
5

-4 -3 -2 -1 O 1 2 3 4
-1
x
-2

-3
-4
-5

(a) On the grid above, sketch the graph of y = f(–x).

(2)
y
5

-4 -3 -2 -1 O 1 2 3 4
-1
x
-2

-3
-4
-5

(b) On the grid above, sketch the graph of y = f(x) – 2

(2)

(Total for question 5 is 4 marks)

6 The graph of y = f(x) is shown on both grids below.

y
5

-4 -3 -2 -1 O 1 2 3 4
-1
x
-2

-3
-4
-5

(a) On the grid above, sketch the graph of y = –f(x).

(2)
y
5

-4 -3 -2 -1 O 1 2 3 4
-1
x
-2

-3
-4
-5

(b) On the grid above, sketch the graph of y = f(x – 1)

(2)

(Total for question 6 is 4 marks)

7 The graph of y = f(x) is shown on the grid.

y
5

-4 -3 -2 -1 O 1 2 3 4
-1
x
-2

-3
-4
-5

(a) On the grid above, sketch the graph of y = f(x – 1).

(1)

The graph of y = f(x) has a turning point at (–1, 2).

(b) Write down the coordinates of the turning point of y = f(–x) + 2

…..........................
(1)

(Total for question 7 is 2 marks)