Question 1:
For a curve y = f(x), describe the following transformations.
Question 1(a): [1 mark]
f(x-1)
Answer type: Multiple choice type 1
A: The graph moves 1 place to the right.
B: The graph moves 1 place to the left.
C: The graph moves 1 place up.
D: The graph moves 1 place down.
ANSWER: A: The graph moves 1 place to the right.
Question 1(b): [1 mark]
f(x)+7
Answer type: Multiple choice type 1
A: The graph moves 7 places to the right.
B: The graph moves 7 places to the left.
C: The graph moves 7 places up.
D: The graph moves 7 places down.
ANSWER: C: The graph moves 7 places up.
Question 1(c): [1 mark]
f(x+5)
Answer type: Multiple choice type 1
A: The graph moves 5 places to the right.
B: The graph moves 5 places to the left.
C: The graph moves 5 places up.
D: The graph moves 5 places down.
ANSWER: B: The graph moves 5 places to the left.
Question 2: [3 marks]
The graph of f(x) has been drawn below.
Match up the following graphs to the labels, A, B and C, from the axes below.
f(x)+2
f(x-3)
f(x+1)-1
Write your answers as a capital letter.
Answer type: Multiple answers type 1
ANSWER:
f(x)+2: A
f(x-3): B
f(x+1)-1: C
Question 3: [3 marks]
The graph of f(x) has been drawn below.
Match up the following graphs to the labels, A, B and C, from the axes below.
f(-x)
-f(x)
f(x-2)
Write your answers as a capital letter.
Answer type: Multiple answers type 1
ANSWER:
f(-x): A
-f(x): C
f(x-2): B
Question 4:
The graph y=f(x) has been drawn below.
Question 4(a): [2 marks]
Find the new co-ordinates of the points A, B, under the following transformation:
-f(x)
Choose the correct answer.
Answer type: Multiple choice type 1
A: A: \, (-2,2) and B: \, (0,-2)
B: A: \, (-2,-2) and B: \, (0,2)
C: A: \, (2,2) and B: \, (0,-2)
D: A: \, (-2,2) and B: \, (0,2)
ANSWER: B: A: \, (-2,-2) and B: \, (0,2)
WORKING:
This is a reflection in the x-axis.
A: \, (-2,2), B: \, (0,-2).
\text{New } A = (-2,-2), \text{New } B = (0,2)
Question 4(b): [2 marks]
Find the new co-ordinates of the points A, B, under the following transformation:
f(x-3)
Chose the correct answer.
Answer type: Multiple choice type 1
A: A: \, (-5,2) and B: \, (-3,-2)
B: A: \, (1,2) and B: \, (3,-2)
C: A: \, (-2,5) and B: \, (0,1)
D: A: \, (-2,-1) and B: \, (0,-5)
ANSWER: B: A: \, (1,2) and B: \, (3,-2)
WORKING:
This is a translation to the right by 3.
A: \, (-2,2), B: \, (0,-2).
\text{New } A = (1,2), \text{New } B = (3,-2)
Question 5:
The graph of y=f(x) has been drawn below.
Question 5(a): [1 mark]
What is the correct transformation of f(x) onto A?
Answer type: Multiple choice type 1
A: f(x+3)
B: f(x-3)
C: f(x)+3
D: f(x)-3
ANSWER: A: f(x+3)
WORKING:
Moves left by 3.
Question 5(b): [1 mark]
What is the correct transformation of f(x) onto B?
Answer type: Multiple choice type 1
A: f(x+3)
B: f(x-3)
C: f(x)+3
D: f(x)-3
ANSWER: D: f(x)-3
WORKING:
Moves down by 3.
Question 5(c): [1 mark]
What is the correct translation to transform A into B?
Answer type: Multiple choice type 1
A: Move right 3, move down 3.
B: Move right 3, move up 3.
C: Move left 3, move up 3.
D: Move left 3, move down 3.
ANSWER: A: Move right 3, move down 3.
Question 6:
The three graphs marked on the axes below are all transformations of y=f(x).
Determine the following transformations that have taken place to transform y=f(x) into the following:
Question 6(a): [1 mark]
y = f(x) into A.
Answer type: Multiple choice type 1
A: f(x+3)
B: f(x-3)
C: f(x)+3
D: f(x)-3
ANSWER: A: f(x+3)
WORKING:
Moves left by 3.
Question 6(b): [1 mark]
y = f(x) into B.
Answer type: Multiple choice type 1
A: f(-x+1)
B: f(-x-1)
C: -f(x)+1
D: -f(x)-1
ANSWER: D: -f(x)-1
WORKING:
Reflected in the x-axis and moved down by 1.