1. Worked examples and Exam practice
Transforming graphs
Worked examples
and
Exam practice
The animated gifs create immediate interest and can increase a pupil’s attention span
worked example 1
worked example 2
worked example 3
worked example 4
worked example 5
Practice question 1
Practice question 2
Practice question 3
Practice question 4

2. worked example 1 Sketch f(x) - 3 f(x) A (-3, 4) A B (0, 0) f(x) - 3
hit return to see the next step
Sketch f(x) - 3
Show where points A, B and C
will be on the new graph
f(x)
A (-3, 4) A
B (0, 0)
f(x) - 3
C (1, -1) B
A (-3, 1)
C (1, -4)
B (0, -3) C
worked example 1

3. worked example 2 Sketch f(x+4) f(x+4) f(x) A (-1, 0) B (1, -3)
hit return to see the next step
Sketch f(x+4)
Show where points A, B and C
will be on the new graph
f(x+4)
f(x)
A (-1, 0)
B (1, -3)
C (3½, 0) A C
A’ (-5, 0)
B’ (-3, -3)
C’ (-½, 0) B

4. worked example 3 Sketch -f(x+4) f(x+4) f(x) A (-1, 0) B (1, -3)
hit return to see the next step
worked example 3
Sketch -f(x+4)
Show where points A, B and C
will be on the new graph
f(x+4)
f(x)
A (-1, 0)
B (1, -3)
C (3½, 0)
First move 4 along
A (-5, 0)
B (-3, -3)
C (-½, 0) A C
Now reflect across
x axis
A’(-5, 0)
B’(-3, 3)
C’(-½, 0) B
-f(x+4)

5. worked example 4 2f(x) Sketch 2f(x) f(x) A (-3, 4) A B (0, 0)
hit return to see the next step
worked example 4
2f(x)
Sketch 2f(x)
Show where points A, B and C
will be on the new graph
f(x)
A (-3, 4) A
B (0, 0)
C (1, -1) B
A’(-3, 8)
C’(1, -2)
B’(0, 0) C

6. worked example 5 Sketch f(4x) A (0, 4) B (8, 0) A B A’ (0, 4)
hit return to see the next step
Sketch f(4x)
Show where points A, B and C
will be on the new graph
A (0, 4)
B (8, 0) A B
A’ (0, 4)
B’ (2, 0)
f(x)
f(4x)

7. Sketch the graph of f(x) + 4
The graph of f(x) = x2+2x - 4
Sketch the graph of f(x) + 4
b) What is the new minimum point of the graph
Practice example 1
f(x)
Answer
(-1,-5)

8. The graph of f(x) is shown below
Practice example 2
The graph of f(x) is shown below
Sketch the graph of f(x - 3), mark any relevant points A B C -3 5
f(x)
Answer

9. The graph of f(x) is shown below
Practice example 3
The graph of f(x) is shown below
Sketch the graph of 2f(x) - 3, note the max point
(0,5)
Answer
f(x)

10. The graph of f(x) is shown below
Practice example 4
The graph of f(x) is shown below
Sketch the graph of f(2x), mark any relevant points
f(x) -6 3
Answer -6

11. Practice example 1 Answer
The graph of f(x) = x2+2x - 4
Sketch the graph of f(x) + 4
b) What is the new minimum
point of the graph
f(x) + 4
f(x)
b) the new minimum
point is (-1,-1)
(-1,-5)

12. Practice example 2 Answer
The graph of f(x) is shown below
Sketch the graph of f(x - 3),
mark any relevant points -3 3 5 8
f(x)
f(x-3)

13. Practice example 3 Answer
The graph of f(x) is shown below
Sketch the graph of 2f(x) - 3,
mark the new max point
(0,7)
(0,5)
f(x)
2f(x)-3

14. Practice example 4 Answer
The graph of f(x) is shown below
Sketch the graph of f(2x),
mark any relevant points
f(2x)
f(x)
1.5 -3 -6 3 -6