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

Starter quiz

$\text{f}(x)+a$ is a ______ of the graph of $\text{f}(x)$ .

'transformation' ✓
Match each piece of function notation to a description.

$\text{f}(x)+4$

⇔

The output of $\text{f}(x)$ has $4$ added to it. ✓

$\text{f}(x+4)$

⇔

The input has $4$ added to it before the function is applied. ✓

$4\text{f}(x)$

⇔

The output of $\text{f}(x)$ is multiplied by $4$ ✓

$\text{f}(x)-4$

⇔

The output of $\text{f}(x)$ has $4$ subtracted from it. ✓

$\text{f}(x-4)$

⇔

The input has $4$ subtracted before the function is applied. ✓
Shape 'a' has been transformed to shape 'b' by translation of __________.

$3$ right, $1$ up.

$8$ right, $3$ up. ✓

$8$ left, $3$ down.

vector $\begin{pmatrix}8 \\ 3\end{pmatrix}$ ✓

vector $\begin{pmatrix}3 \\ 8\end{pmatrix}$
The transformation of the point $(3,-2)$ to the position $(-4,-2)$ could be described by __________.

translation by $7$ in the positive $x$ -direction.

translation by $7$ in the negative $x$ -direction. ✓

translation by $7$ in the negative $y$ -direction.

translation by vector $\begin{pmatrix}-7 \\ 0\end{pmatrix}$ ✓

reflection in the line $x=-1$
The point $(-1,13)$ is translated $+8$ in the $x$ -direction. What is its new position?

$(7,13)$ ✓

$(-9,13)$

$(-1,21)$

$(-1,5)$

$(8,13)$
The point $(c,-d)$ is translated by $9$ in the negative $x$ -direction. What is its new position?

$(c,9-d)$

$(c,-d-9)$

$(-9,-d)$

$(c-9,-d)$ ✓

$(c+9,-d)$

Exit quiz

$\text{f}(x+a)$ is a transformation by __________.

reflection

rotation

translation ✓

enlargement
$\text{f}(x+a)$ is a transformation by translation of __________.

$a$ in the $x$ -direction.

$-a$ in the $x$ -direction. ✓

$a$ in the $y$ -direction.

$-a$ in the $y$ -direction.
$y=\text{f}(x)$ is graphed. Which of these images shows the transformation $y=\text{f}(x-3)$ ?
$<Math>y=\text{f}(x)</Math> is graphed here. Which coordinate pairs will be on the transformation <Math>y=\text{f}(x+6)</Math>?$

$y=\text{f}(x)$ is graphed here. Which coordinate pairs will be on the transformation $y=\text{f}(x+6)$ ?

$(-5,-4)$

$(-11,-10)$ ✓

$(4,-1)$

$(-6,5)$ ✓

$(0,-1)$
$<Math>y=\text{f}(x)</Math> is graphed. What transformation can we see graphed? <Math>y=</Math><span class="blank">______</span>$

$y=\text{f}(x)$ is graphed. What transformation can we see graphed? $y=$ ______

'f(x-7)' ✓
$<Math>y=\text{f}(x)</Math> is graphed here. Which could the graph of the transformation be?$

$y=\text{f}(x)$ is graphed here. Which could the graph of the transformation be?

$y=\text{f}(x+45)$

$y=\text{f}(x+90)$ ✓

$y=\text{f}(x-90)$

$y=\text{f}(x-270)$ ✓

$y=\text{f}(x+270)$

Worksheet

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Video

Lesson Details

Key learning points

Desmos is an effective tool for showing the effects of this transformation
The actual function itself does not need to be known
The graph is transformed by a horizontal translation in the opposite direction

Common misconception

f $(x)+5$ is a translation of $+5$ in the $y$ -direction so pupils may assume that f $(x+5)$ is a translation of $+5$ in the $x$ -direction.

Visually showing pupils, using graphing technology, that f $(x+5)$ is not a translation to the right will help. Showing them a comparison of the two tables of values for both functions shows them why this happens.

Keywords

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.