The Robert Smyth School
Mathematics Faculty
Y11 Topic 16
Transformations of Graphs
Innovation & excellence
Name:
Grade A*
Transformations of Graphs
1.
Teacher
Assessment
The sketch below is of the graph of y = x2
y
O
x
On the axes provided, sketch the following graphs.
The graph of y = x2 is shown dotted on each set of axes to act as a guide.
(a)
y = x2 + 2
y
O
x
(1)
(b)
y = (x – 2)2
y
O
x
(1)
The Robert Smyth School
1
The Robert Smyth School
Mathematics Faculty
Y11 Topic 16
Transformations of Graphs
Innovation & excellence
(c)
1
y  x2
2
y
O
x
(1)
(Total 3 marks)
2.
The diagrams, which are not drawn to scale, show the graph of y = x2 and four
other graphs A, B, C and D.
A, B, C and D represent four different transformations of y = x2.
Find the equation of each of the graphs A, B, C and D.
y
Graph A
y = x2
O
Answer
3
x
Graph A is y = .........................
y
Graph B
y = x2
–3
Answer
The Robert Smyth School
O
x
Graph B is y = .........................
2
The Robert Smyth School
Mathematics Faculty
Y11 Topic 16
Transformations of Graphs
Innovation & excellence
y
y = x2
O
x
Graph C
Answer
Graph C is y = .........................
y
3
y = x2
O
x
Graph D
Answer
Graph D is y = .........................
(Total 4 marks)
3.
The graph y = x2 is transformed as shown.
y
y
Not drawn
accurately
y = x2
O
x
(–3,0) O
x
Write down the equation of the transformed graph.
Answer y = ....................................................
(1)
(Total 1 mark)
The Robert Smyth School
3
The Robert Smyth School
Mathematics Faculty
Y11 Topic 16
Transformations of Graphs
Innovation & excellence
4.
The diagram shows the graph of y = x2 for 2  x  2.
y
5
–5
5 x
0
–5
Each of the graphs below is a transformation of this graph.
Write down the equation of each graph.
y
5
(a)
–5
y
5
(b)
–5
5 x
0
–5
0
5 x
–5
y
5
–5
0
5 x
(c)
–5
Answer (a) y = ....................................................
(1)
Answer (b) y = ....................................................
(1)
Answer (c) y = ....................................................
(1)
(Total 3 marks)
The Robert Smyth School
4
The Robert Smyth School
Mathematics Faculty
Y11 Topic 16
Transformations of Graphs
Innovation & excellence
5.
This is the graph of y = sin x.
y
1
0
0°
90°
180°
270°
360° x
–1
On the grid below, sketch the graph of y = sin (x - 90)
y
1
0
0°
90°
180°
270°
360° x
–1
(Total 2 marks)
6.
This is the graph of y = cos x for 0°  x  360°
y
1
90
O
180
270
x
360
–1
(a)
On the axes below draw the graph of y = cos(x – 90) for 0°  x  360°
y
1
O
90
180
270
360
x
–1
(2)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Y11 Topic 16
Transformations of Graphs
Innovation & excellence
(b)
Write down a possible equation of the following graph.
y
1
90
O
180
270
x
360
–1
Answer ……………………………………………
(1)
(Total 3 marks)
7.
This is the graph of y = cos x for 0°  x  360°
y
2
1
0
90
180
270
360 x
–1
–2
Write the equation of each of the transformed graphs.
In each case the graph of y = cos x is shown dotted to help you.
(a)
y
2
1
0
90
180
270
360 x
–1
–2
Equation y = ..............................................................
(1)
The Robert Smyth School
6
The Robert Smyth School
Mathematics Faculty
Y11 Topic 16
Transformations of Graphs
Innovation & excellence
(b)
y
2
1
0
90
180
270
360 x
–1
–2
Equation y = ..............................................................
(1)
(c)
y
2
1
0
90
180
270
360 x
–1
–2
Equation y = ..............................................................
(1)
(d)
y
2
1
0
90
180
270
360 x
–1
–2
Equation y = ..............................................................
(1)
(Total 4 marks)
The Robert Smyth School
7
The Robert Smyth School
Mathematics Faculty
Y11 Topic 16
Transformations of Graphs
Innovation & excellence
8.
The diagram shows the graph of y = sin x° for 0 < x < 360
y
3
2
1
0
90
180
270
360 x
270
360 x
–1
–2
–3
On the axes below sketch the following graphs.
(a)
y = 2 sin x° for 0 < x < 360
y
3
2
1
0
90
180
–1
–2
–3
(1)
The Robert Smyth School
8
The Robert Smyth School
Mathematics Faculty
Y11 Topic 16
Transformations of Graphs
Innovation & excellence
(b)
y = sin 2x° for 0 < x < 360
y
3
2
1
0
90
180
270
360 x
–1
–2
–3
(1)
(c)
y = 2 + sin x° for 0 < x < 360
y
3
2
1
0
90
180
270
360 x
–1
–2
–3
(1)
(Total 3 marks)
The Robert Smyth School
9
The Robert Smyth School
Mathematics Faculty
Y11 Topic 16
Transformations of Graphs
Innovation & excellence
9.
The graph of y = sin x for 0°  x  360° is shown on the grid below.
The point P(90, 1) lies on the curve.
y
2
1
O
P
90
180
270
360
x
360
x
–1
–2
On both of the grids that follow, sketch the graph of the transformed function.
In both cases write down the coordinates of the transformed point P.
(a)
y = sin (x – 45)
y
2
1
O
90
180
270
–1
–2
P (......................., ......................)
(2)
The Robert Smyth School
10
The Robert Smyth School
Mathematics Faculty
Y11 Topic 16
Transformations of Graphs
Innovation & excellence
(b)
y = 2sinx
y
2
1
O
90
180
270
360
x
–1
–2
P (......................., ......................)
(2)
(Total 4 marks)
10.
This is the graph of y = sin x for 0°  x  360°
y
3
2
1
0
x
90
180
270
360
–1
–2
–3
The Robert Smyth School
11
The Robert Smyth School
Mathematics Faculty
Y11 Topic 16
Transformations of Graphs
Innovation & excellence
Draw the graphs indicated for 0°  x  360° In each case the graph of y = sinx is shown to help.
(a)
y = 2 sinx
y
3
2
1
0
x
90
180
270
360
–1
–2
–3
(1)
(b)
y = - sinx
y
3
2
1
0
x
90
180
270
360
–1
–2
–3
(1)
(c)
y = sin 2x
y
3
2
1
0
x
90
180
270
360
–1
–2
–3
(1) (Total 3 marks)
Success:
The Robert Smyth School
Target:
12