Transforming graphs: y = f(ax) | Maths | Quizalize & Oak National Academy

Starter quiz

$a\text{f}(x)$ is a transformation of the graph of $\text{f}(x)$ by a __________ in the $y$ -direction.

stretch ✓

reflection

translation

rotation
Match each piece of function notation to a description.

$\text{f}(x)+15$

⇔

The output of $\text{f}(x)$ has $15$ added to it. ✓

$\text{f}(x+15)$

⇔

The input has $15$ added to it before the function is applied. ✓

$15\text{f}(x)$

⇔

The output of $\text{f}(x)$ is multiplied by $15$ . ✓

$\text{f}(15x)$

⇔

The input is multiplied by $15$ before the function is applied ✓
Shape 'b' is an enlargement of shape 'a' by scale factor of...

$2$

$1\over2$ ✓

$-2$
$Shape 'a' is enlarged by scale factor <Math>1\over4</Math> from centre of enlargement <Math>(0,0)</Math>. Which of these coordinate pairs will be vertices of the enlargement?$

Shape 'a' is enlarged by scale factor $1\over4$ from centre of enlargement $(0,0)$ . Which of these coordinate pairs will be vertices of the enlargement?

$(1,0)$ ✓

$(1,4)$

$(4,1)$

$(1,1)$ ✓

$(2,0)$ ✓
A square of area $144$ square units is enlarged by a scale factor of $\frac{1}{3}$ . What is the area of the transformed square? ______

'16' ✓
$Shape 'a' is enlarged by scale factor <Math>1\over2</Math> from centre of enlargement <Math>(-2,0)</Math>. What will the new position of the marked vertex be?$

Shape 'a' is enlarged by scale factor $1\over2$ from centre of enlargement $(-2,0)$ . What will the new position of the marked vertex be?

$(-1,-4)$

$(-1,-2)$

$(-2,-2)$ ✓

$\left(-2,{1\over2}\right)$

Exit quiz

$y=\text{f}(ax)$ will transform $y=\text{f}(x)$ by stretch in the ______-direction.

'x' ✓
The transformation $\text{f}(ax)$ is a stretch of $\text{f}(x)$ in the $x$ -direction by a ______ of $1\over{a}$ .

'scale factor' ✓
$<Math>y=\text{f}(x)</Math> is graphed here. Which coordinate pairs will be on the graph <Math>y=\text{f}(4x)</Math>?$

$y=\text{f}(x)$ is graphed here. Which coordinate pairs will be on the graph $y=\text{f}(4x)$ ?

$(0,1)$

$(0,16)$

$(1,5)$ ✓

$(16,5)$

$(-1,3)$ ✓
$y=\text{f}(x)$ is graphed. Which of these images shows the transformation $y=\text{f}(3x)$ ?
$<Math>\text{f}(x)=\text{cos}(x)</Math>. Which points will be on the graph <Math>y=\text{f}(10x)</Math>?$

$\text{f}(x)=\text{cos}(x)$ . Which points will be on the graph $y=\text{f}(10x)$ ?

$(0,1)$ ✓

$(0,10)$

$(36,1)$ ✓

$(360,10)$

$(360,0.1)$
$<Math>\text{f}(x)=\text{cos}(x)</Math>. In the domain <Math>0\leq{x}\leq360</Math> how many points on the graph of <Math>y=\text{f}(10x)</Math> will have an <Math>x</Math> coordinate value of <Math>1</Math>?$

$\text{f}(x)=\text{cos}(x)$ . In the domain $0\leq{x}\leq360$ how many points on the graph of $y=\text{f}(10x)$ will have an $x$ coordinate value of $1$ ?

'11' ✓

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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 1/a in the x-direction

Common misconception

Pupils confuse 'stretch' transformations. Does the transformation $y=$ f $(ax)$ affect the $x$ or $y$ coordinates?

Interpreting the notation is key. $y=$ f $(ax)$ is the input of f $(x)$ being multiplied by $a$ . Which coordinate is the input?

Keywords

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