Transforming graphs: y = af(x) | Maths | Quizalize & Oak National Academy

Starter quiz

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

reflection

rotation

translation ✓

enargement
Match each piece of function notation to a description.

$\text{f}(x)+2$

⇔

The output of $\text{f}(x)$ has $2$ added to it. ✓

$\text{f}(x+2)$

⇔

The input has $2$ added to it before the function is applied. ✓

$-\text{f}(x)$

⇔

The output of $\text{f}(x)$ is multiplied by $-1$ . ✓

$\text{f}(-x)$

⇔

The input is multiplied by $-1$ before the function is applied. ✓

$2\text{f}(x)$

⇔

The output of $\text{f}(x)$ is multiplied by $2$ . ✓
Shape 'b' is an enlargement by a scale factor of ______ of shape 'a'.

'4' ✓
Shape 'a' is enlarged by scale factor $2$ from centre of enlargement $(0,0)$ . Which of these coordinate pairs will be vertices of the enlargement?

$(2,2)$

$(8,2)$

$(8,0)$ ✓

$(8,4)$ ✓

$(6,0)$
Shape 'a' is enlarged by scale factor $5$ from centre of enlargement $(0,0)$ . Which of these coordinate pairs will be vertices of the enlargement?

$(0,5)$

$(15,0)$

$(0,15)$ ✓

$(35,0)$

$(0,35)$ ✓
Shape 'a' is enlarged by scale factor $8$ from centre of enlargement $(-3,0)$ . What will the new position of the marked vertice be? Give your answer in the form $(x,y)$ ______

'(-3, -16)' ✓

Exit quiz

$y=a\text{f}(x)$ will transform $y=\text{f}(x)$ by __________ in the $y$ -direction.

translation

rotation

reflection

a stretch ✓
The transformation $a\text{f}(x)$ is a stretch of $\text{f}(x)$ in the $y$ -direction by a scale factor of ______.

'a' ✓
$<Math>y=\text{f}(x)</Math> is graphed here. Which coordinate pairs will be on the graph of <Math>y=2\text{f}(x)</Math>?$

$y=\text{f}(x)$ is graphed here. Which coordinate pairs will be on the graph of $y=2\text{f}(x)$ ?

$(0,-4)$

$(0,-8)$ ✓

$(2,0)$ ✓

$(1,0)$

$(3,4)$ ✓
$y=\text{f}(x)$ is graphed. Which of these images shows the transformation $y=2\text{f}(x)$ ?
$<Math>\text{f}(x)=\text{cos}(x)</Math> Which points are invariant after the transformation <Math>y=4\text{f}(x)</Math>?$

$\text{f}(x)=\text{cos}(x)$ Which points are invariant after the transformation $y=4\text{f}(x)$ ?

$(0,1)$

$(90,0)$ ✓

$(180,-1)$

$(270,0)$ ✓

$(360,4)$
$(24,40)$ is a point on the line $y=8\text{f}(x)$ . What was the position of this point on the line $y=\text{f}(x)$ before the transformation? Give your answer in the form $(x,y)$ .

'(24, 5)' ✓

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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 stretched by a scale factor of a in the y-direction

Common misconception

Pupils confuse 'stretch' transformations. Many transformations of the form $y=a$ f $(x)$ have the appearance of a compression towards the $y$ -axis rather than a 'stretch' in the $y$ -direction.

Interpreting the notation is key. $y=a$ f $(x)$ is the output of f $(x)$ being multiplied by $a$ . Which coordinate is the output? The $y$ coordinates change by a scale factor of $a$ so this must be a stretch in the $y$ -direction.

Keywords

Transformation - A transformation is a process that may change the size, orientation or position of a shape.