Practise Transforming graphs. 1 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
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Write down the coordinates of the point on \(y = f(x + 3)\) that corresponds to \((2, -1)\).
\((-1, -1)\)
Sample questions
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy2 marks
The graph of \(y = f(x)\) has a maximum point at \((-2, -4)\).
(a) Write down the coordinates of the turning point of the graph of \(y = f(x) - 4\).[1]
(b) Describe the transformation that maps the graph of \(y = f(x)\) onto the graph of \(y = f(x) - 4\).[1]
Show the answer and mark scheme
(a)Answer: \((-2, -8)\)
B1 for \((-2, -8)\)
Worked solution: \(y = f(x) - 4\) is a translation by vector \(\begin{pmatrix} 0 \\ -4 \end{pmatrix}\), so \((-2, -4)\) maps to \((-2, -8)\).
(b)Answer: translation 4 units down (vector \(\begin{pmatrix} 0 \\ -4 \end{pmatrix}\))
B1 for translation by \(\begin{pmatrix} 0 \\ -4 \end{pmatrix}\) oe, e.g. 4 units down
Worked solution: Subtracting 4 from every \(y\)-value moves the graph 4 units down.
Question 2Medium2 marks
The graph of \(y = f(x)\) passes through the point \((2, -1)\). Aimee says, 'The graph of \(y = f(x + 3)\) is the graph of \(y = f(x)\) translated 3 units to the right.'
(a) Explain why Aimee is wrong.[1]
(b) Write down the coordinates of the point on \(y = f(x + 3)\) that corresponds to \((2, -1)\).[1]
Show the answer and mark scheme
(a)Answer: \(y = f(x + 3)\) is a translation 3 units to the left, by the vector \(\begin{pmatrix} -3 \\ 0 \end{pmatrix}\).
C1 for stating that it is a translation 3 units to the left (vector \(\begin{pmatrix} -3 \\ 0 \end{pmatrix}\))
Worked solution: On \(y = f(x + 3)\), the same \(y\)-value is reached 3 units earlier: when \(x + 3 = 2\), i.e. \(x = -1\). So the graph moves 3 units to the left.
(b)Answer: \((-1, -1)\)
B1 for \((-1, -1)\)
Worked solution: \((2 - 3, -1) = (-1, -1)\)
Question 3Hard5 marks
The graph of \(y = f(x)\) has a minimum point at \((-2, -5)\).
(a) Write down the coordinates of the turning point of the graph of \(y = 3 - f(x)\).[2]
(b) Write down the coordinates of the turning point of the graph of \(y = f(-x) + 3\).[2]
(c) Is the turning point of the graph of \(y = 3 - f(x)\) a maximum or a minimum? Give a reason for your answer.[1]
Show the answer and mark scheme
(a)Answer: \((-2, 8)\)
B2 for \((-2, 8)\) (B1 for one coordinate correct)
Worked solution: \(y = 3 - f(x)\) is a reflection in the \(x\)-axis followed by a translation by vector \(\begin{pmatrix} 0 \\ 3 \end{pmatrix}\), so \((-2, -5)\) maps to \((-2, 8)\).
(b)Answer: \((2, -2)\)
B2 for \((2, -2)\) (B1 for one coordinate correct)
Worked solution: \(y = f(-x) + 3\) is a reflection in the \(y\)-axis followed by a translation by vector \(\begin{pmatrix} 0 \\ 3 \end{pmatrix}\), so \((-2, -5)\) maps to \((2, -2)\).
(c)Answer: maximum: reflecting in the \(x\)-axis turns a minimum into a maximum
C1 for maximum with a correct reason
Worked solution: A reflection in the \(x\)-axis turns the graph upside down, so the minimum becomes a maximum.