GCSE · Graphs of functions

Transformations of graphs (y = f(x) + a, y = f(x + a), y = −f(x), y = f(−x))Exam-style questions

Move a graph without plotting it again. A number added outside the f moves the curve up or down; a number added inside the bracket moves it sideways, the opposite way to its sign; a minus sign outside reflects it in the x-axis and a minus sign inside reflects it in the y-axis. Track the key points, describe each change fully, combine two changes, write the new equation, and use the same four rules on the sine and cosine waves.

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20 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The graph of $y = \mathrm{f}(x)$ has a maximum point at $(-2, 5)$

Write down the coordinates of the turning point of the graph of
(a) $y = \mathrm{f}(x) - 7$

(1 mark)
(b) $y = \mathrm{f}(x + 3)$

(1 mark)
(c) $y = -\mathrm{f}(x)$

(1 mark)
(d) $y = \mathrm{f}(-x)$

(1 mark)
Level 3 · 4 marksTry it
2
(a) The sketch shows the graph of $y = \sin x + a$ for $0° \le x \le 360°$ , where $a$ is a constant.Write down the value of $a$ .

(1 mark)
(b) The sketch shows the graph of $y = \cos(x + b)$ for $0° \le x \le 360°$ , where $0 < b < 180$ Find the value of $b$ .

(2 marks)
Level 3 · 3 marksTry it
3
Here is a question and an incorrect solution.

Question: Describe fully the single transformation that maps the graph of $y = x^2$ onto the graph of $y = (x + 5)^2 - 2$

Solution: Translation by the vector $\begin{pmatrix} 5 \\ -2 \end{pmatrix}$
(a) Describe the error made.

(1 mark)
(b) Write down the correct vector.

(1 mark)
(c) Write down the coordinates of the turning point of the graph of $y = (x + 5)^2 - 2$

(1 mark)
Level 3 · 3 marksTry it
4
The graph of $y = \cos x$ is translated $90°$ to the right.
(a) Write down the equation of the new graph.

(1 mark)
(b) Write down the coordinates of the point where the new graph crosses the $y$ -axis.

(1 mark)
(c) Asha says,

"The new graph is the graph of $y = \sin x$ "

Is she correct?

Give a reason for your answer.

(1 mark)
Level 3 · 3 marksTry it
5
The curve $C$ has equation $y = x^2 + 2x - 8$

$C$ is translated by the vector $\begin{pmatrix} 3 \\ 0 \end{pmatrix}$ to give the curve $D$ .

Find the equation of $D$ .

Give your answer in the form $y = x^2 + bx + c$

You must show your working.

(3 marks)
Level 3 · 3 marksTry it

2 more questions on transformations of graphs (y = f(x) + a, y = f(x + a), y = −f(x), y = f(−x))

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