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
(a) The graph of $y = x^2$ is translated by the vector $\begin{pmatrix} 0 \\ -6 \end{pmatrix}$

Write down the equation of the new graph.

(1 mark)
(b) The graph of $y = x^2$ is translated by the vector $\begin{pmatrix} 5 \\ 0 \end{pmatrix}$

Write down the equation of the new graph.

(1 mark)
Level 2 · 2 marksTry it
2
The curve $C$ has equation $y = x^2 - 6x$

A reflection of $C$ in the $x$ -axis gives the curve $D$ .

A reflection of $C$ in the $y$ -axis gives the curve $E$ .
(a) Find an equation for $D$ .

(1 mark)
(b) Find an equation for $E$ .

(1 mark)
Level 2 · 2 marksTry it
3
The grid shows the graph of $y = \mathrm{f}(x)$ for $-3 \le x \le 2$ (a) On the grid, draw the graph of $y = \mathrm{f}(x) - 3$

(1 mark)
(b) On the grid, draw the graph of $y = -\mathrm{f}(x)$

(1 mark)
Level 2 · 2 marksTry it
4
(a) Describe fully the single transformation that maps the graph of $y = \mathrm{f}(x)$ onto the graph of $y = \mathrm{f}(x - 3)$

(2 marks)
(b) Describe fully the single transformation that maps the graph of $y = \mathrm{f}(x)$ onto the graph of $y = -\mathrm{f}(x)$

(1 mark)
Level 2 · 3 marksTry it
5
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

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

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