Transforming graphs: y = f(x) + a | Maths | Quizalize & Oak National Academy

Starter quiz

When every point of a shape moves the same distance in the same direction the transformation is called a...

translation ✓

reflection

rotation

enlargement
Match each piece of function notation to a description.

$\text{f}(x)+11$

⇔

The output of $\text{f}(x)$ has $11$ added to it. ✓

$\text{f}(x+11)$

⇔

The input has $11$ added to it before the function is applied. ✓

$11\text{f}(x)$

⇔

The output of $\text{f}(x)$ is multiplied by $11$ ✓

$\text{f}(x)-11$

⇔

The output of $\text{f}(x)$ has $11$ subtracted from it. ✓

$\text{f}(x-11)$

⇔

The input has $11$ subtracted before the function is applied. ✓
Shape 'a' has been transformed to shape 'b' by a translation of...

$2$ right, $1$ down.

$4$ right, $6$ down. ✓

$4$ left, $6$ up.

vector $\begin{pmatrix}4 \\ 6\end{pmatrix}$

vector $\begin{pmatrix}4 \\ -6\end{pmatrix}$ ✓
For the function $\text{f}(x)$ , $\text{f}(8)=37$ , match these transformations of the function to their values.

$\text{f}(8)+3$

⇔

$40$ ✓

$3\text{f}(8)$

⇔

$111$ ✓

$\text{f}(8)-3$

⇔

$34$ ✓

$-3\text{f}(8)$

⇔

$-111$ ✓

$3\text{f}(8)-3$

⇔

$108$ ✓
The point $(4,1)$ is translated 'up $5$ '. What is it's new position?

$(4,6)$ ✓

$(9,6)$

$(4,5)$

$(9,1)$
The point $(-5,-a)$ is translated 'down $4$ '. What is it's new position?

$(-1,-a)$

$(-9,-a)$

$(-5,-4)$

$(-5,-a-4)$ ✓

$(-5,a-4)$

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Pupils may not see the vertical translation depending on the function used to show the effect of $a$ .

Ensure pupils consider a range of functions so that they can see the movement of the graph.

Function - A function is a mathematical relationship that uniquely maps values of one set to the values of another set.
Transformation - A transformation is a process that may change the size, orientation or position of a shape or graph.