GCSE Identifying Graphs and Transformations of Curves Worksheet
1. Each equation in the table represents
one of the graphs A to F.
Write the letter of each graph in the
correct place in the table.
3. Below is a sketch of 𝑦 = 𝑓(𝑥). On the
provided axis, sketch 𝑦 = 𝑓(𝑥 + 1) + 5
and 𝑓(𝑥 − 3) − 4 , indicating the
coordinates of A in each case.
y
𝑦 = 𝑓(𝑥)
A
x
(2, 0)
Equation
Graph
y = 4 sin x°
y = 4 cos x°
y = x2 – 4x + 5
y = 4 × 2x
3
y=x +4
y=
4
x
2. [Edexcel May 2009] The grid shows
the graph of y = cos x° for values of x
from 0 to 540. On the grid, sketch the
graph of y = 3 cos (2x°) for values of x
from 0 to 540.
4. Given the sketch below of 𝑦 = 𝑓(𝑥),
sketch the following transformations,
indicating the coordinates of A, B and
C.
𝑦 = 𝑓(𝑥)
𝐵(0,3)
𝐴(−2,1)
𝑦 = −𝑓(𝑥)
𝐶(2,0)
𝑦 = 𝑓(𝑥 − 2)
𝑦 = 𝑓(2𝑥)
5. For the given functions 𝑦 = 𝑓(𝑥),
sketch the transformed function on
the same axis.
𝑦
2
6.
𝑦
2
2
𝑥
Sketch 𝑦 = 𝑓(𝑥) + 1
2
𝑥
Match the following equations to the
following features (some features
might match multiple equations).
Indicate your answer by connecting
the two with a line.
y = x2
Has a y-intercept of 1.
y = 5x
Has a y-intercept of 8.
y = 2x + 1
Has a line of
symmetry.
Sketch 𝑦 = 𝑓(2𝑥)
y = x3 + x2 – 10x + 8
𝑦
𝑦
y = x2 + 3
y = 2/x
2
𝑥
Sketch 𝑦 = 𝑓(𝑥 − 1)
2
𝑥
Crosses or touches the
x-axis.
𝑦
2
𝑥
Sketch 𝑦 = 𝑓(−𝑥) − 1
2
𝑥
Sketch 𝑦 = −𝑓(𝑥 + 1)
𝑦
𝑦
2
Sketch 𝑦 = 𝑓(2𝑥) − 1
𝑥
Is parallel to the line
2x - 3.
Is straight.
Sketch 𝑦 = 2𝑓(𝑥)
𝑦
Has an asymptote at
y=0
2
Sketch 𝑦 = −𝑓(−𝑥)
𝑥
ANSWERS
1. Each equation in the table represents
one of the graphs A to F.
Write the letter of each graph in the
correct place in the table.
3. Below is a sketch of 𝑦 = 𝑓(𝑥). On the
provided axis, sketch 𝑦 = 𝑓(𝑥 + 1) +
5 and 𝑓(𝑥 − 3) − 4 , indicating the
coordinates of A in each case.
y
𝑦 = 𝑓(𝑥)
A
x
(2, 0)
A(1, 5)
Equation
Graph
y = 4 sin x°
E
y = 4 cos x°
B
y = x – 4x + 5
F
2
x
C
y = x3 + 4
D
4
y=
x
A
y=4×2
2. [Edexcel May 2009] The grid shows
the graph of y = cos x° for values of x
from 0 to 540. On the grid, sketch the
graph of y = 3 cos (2x°) for values of x
from 0 to 540.
A(5, -4)
4. Given the sketch below of 𝑦 = 𝑓(𝑥),
sketch the following transformations,
indicating the coordinates of A, B and
C.
5. For the given functions 𝑦 = 𝑓(𝑥),
sketch the transformed function on
the same axis.
𝑦
2
𝑦 = 𝑓(𝑥)
𝑦
2
𝐵(0,3)
𝐴(−2,1)
2
𝐶(2,0)
𝑥
Sketch 𝑦 = 𝑓(𝑥) + 1
𝑦 = −𝑓(𝑥)
𝑦 = 𝑓(𝑥 − 2)
𝐴(−2, −1)
𝑥
2
𝑥
2
𝑥
Sketch 𝑦 = 𝑓(2𝑥)
𝑦
𝐵(2,3)
𝐶(2,0)
2
𝑦
2
𝑥
𝐴(0,1)
𝐶(4,0)
𝐵(0, −3)
Sketch 𝑦 = 𝑓(𝑥 − 1)
Sketch 𝑦 = 2𝑓(𝑥)
𝐵(0,3)
𝑦
𝑦
𝑦 = 𝑓(2𝑥)
𝐴(−1,1)
𝐶(1,0)
2
𝑥
Sketch 𝑦 = 𝑓(−𝑥) − 1
Sketch 𝑦 = −𝑓(𝑥 + 1)
𝑦
𝑦
2
Sketch 𝑦 = 𝑓(2𝑥) − 1
𝑥
2
Sketch 𝑦 = −𝑓(−𝑥)
𝑥
6.
Match the following equations to the
following features (some features
might match multiple equations).
Indicate your answer by connecting
the two with a line.
y = x2
Has a y-intercept of 1.
y = 5x
Has a y-intercept of 8.
y = 2x + 1
Has a line of
symmetry.
y = x3 + x2 – 10x + 8
y = x2 + 3
y = 2/x
Has an asymptote at
y=0
Is parallel to the line
2x - 3.
Is straight.
Crosses or touches the
x-axis.