IB Standard Level IB Function Transformation Questions
#1.
The diagram shows the graph of y = f (x), with the x-axis as an asymptote.
y
B(5, 4)
x
A(–5, –4)
(a)
On the same axes, draw the graph of y =f (x + 2) – 3, indicating the coordinates of the
images of the points A and B.
(b)
Write down the equation of the asymptote to the graph of y = f (x + 2) – 3.
(Total 4 marks)
1
2.
The following diagram shows the graph of y = f (x). It has minimum and maximum points at
1
(0, 0) and ( 1, ).
2
y
3.5
3
2.5
2
1.5
1
0.5
–2
–1
0
1
2
3
x
–0.5
–1
–1.5
–2
–2.5
3
.
2
(a)
On the same diagram, draw the graph of y  f ( x – 1) 
(b)
What are the coordinates of the minimum and maximum points of
3
y  f ( x – 1)  ?
2
(Total 4 marks)
2
#3.
The diagram shows parts of the graphs of y = x2 and y = 5 – 3(x – 4)2.
y
y = x2
8
6
y = 5 – 3(x–4)
2
4
2
–2
0
2
4
6
x
The graph of y = x2 may be transformed into the graph of y = 5 – 3(x – 4)2 by these
transformations.
A reflection in the line y = 0
a vertical stretch with scale factor k
a horizontal translation of p units
a vertical translation of q units.
followed by
followed by
followed by
Write down the value of k, p and q.
(Total 4 marks)
3
#4.
The sketch shows part of the graph of y = f (x) which passes through the points A(–1, 3), B(0,
2), C(l, 0), D(2, 1) and E(3, 5).
8
7
6
E
5
4
A
3
B
2
D
1
C
–4
–3
–2
–1
0
1
2
3
4
5
–1
–2
A second function is defined by g (x) = 2f (x – 1).
(a)
Calculate g (0), g (1), g (2) and g (3).
(b)
On the same axes, sketch the graph of the function g (x).
(Total 6 marks)
#5.
The quadratic function f is defined by f (x) = 3x2 – 12x + 11.
(a)
Write f in the form f (x) = 3(x – h)2 – k.
(b)
The graph of f is translated 3 units in the positive x-direction and 5 units in the positive
y-direction. Find the function g for the translated graph, giving your answer in the form
g (x) = 3(x – p)2 + q.
(Total 6 marks)
4
IB Higher Level Function Transformation Questions
#1.
The quadratic function f(x) = p + qx – x2 has a maximum value of 5 when x = 3.
(a)
Find the value of p and the value of q.
(4)
(b)
The graph of f(x) is translated 3 units in the positive direction parallel to the x-axis.
Determine the equation of the new graph.
(2)
(Total 6 marks)
#2.
The diagram below shows the graph of the function y = f(x), defined for all x 
where b > a > 0.
Consider the function g(x) =
(a)
,
1
.
f ( x  a)  b
Find the largest possible domain of the function g.
(2)
(b)
On the same set of axes, sketch the graph of y = g(x). On the graph, indicate any
asymptotes and local maxima or minima, and write down their equations and coordinates.
(6)
(Total 8 marks)
5