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Year 11
Higher

Transforming graphs: y = f(ax)

I can recognise the effect of applying the transformation y = f(ax) to a graph.

icon-background-square
New
New
Year 11
Higher

Transforming graphs: y = f(ax)

I can recognise the effect of applying the transformation y = f(ax) to a graph.

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These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

  1. Desmos is an effective tool for showing the effects of this transformation
  2. The actual function itself does not need to be known
  3. The graph is stretched by a scale factor of 1/a in the x-direction

Keywords

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

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?


To help you plan your year 11 maths lesson on: Transforming graphs: y = f(ax), download all teaching resources for free and adapt to suit your pupils' needs...

Visually showing pupils $$y=$$f$$(ax)$$ using graphing technology demonstrates that it is a stretch in the $$x$$-direction by a scale factor of $$\\frac{1}{a}$$. Showing pupils the comparison of two tables of values explains why this occurs.
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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
$$a\text{f}(x)$$ is a transformation of the graph of $$\text{f}(x)$$ by a __________ in the $$y$$-direction.
Correct answer: stretch
reflection
translation
rotation
Q2.
Match each piece of function notation to a description.
Correct Answer:$$\text{f}(x)+15$$,The output of $$\text{f}(x)$$ has $$15$$ added to it.
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The output of $$\text{f}(x)$$ has $$15$$ added to it.

Correct Answer:$$\text{f}(x+15)$$,The input has $$15$$ added to it before the function is applied.
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The input has $$15$$ added to it before the function is applied.

Correct Answer:$$15\text{f}(x)$$,The output of $$\text{f}(x)$$ is multiplied by $$15$$.
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The output of $$\text{f}(x)$$ is multiplied by $$15$$.

Correct Answer:$$\text{f}(15x)$$,The input is multiplied by $$15$$ before the function is applied
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The input is multiplied by $$15$$ before the function is applied

Q3.
Shape 'b' is an enlargement of shape 'a' by scale factor of...
An image in a quiz
$$2$$
Correct answer: $$1\over2$$
$$-2$$
Q4.
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?
An image in a quiz
Correct answer: $$(1,0)$$
$$(1,4)$$
$$(4,1)$$
Correct answer: $$(1,1)$$
Correct answer: $$(2,0)$$
Q5.
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?
Correct Answer: 16, 16 square units
Q6.
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?
An image in a quiz
$$(-1,-4)$$
$$(-1,-2)$$
Correct answer: $$(-2,-2)$$
$$\left(-2,{1\over2}\right)$$

6 Questions

Q1.
$$y=\text{f}(ax)$$ will transform $$y=\text{f}(x)$$ by stretch in the -direction.
Correct Answer: x, X
Q2.
The transformation $$\text{f}(ax)$$ is a stretch of $$\text{f}(x)$$ in the $$x$$-direction by a of $$1\over{a}$$.
Correct Answer: scale factor
Q3.
$$y=\text{f}(x)$$ is graphed here. Which coordinate pairs will be on the graph $$y=\text{f}(4x)$$?
An image in a quiz
$$(0,1)$$
$$(0,16)$$
Correct answer: $$(1,5)$$
$$(16,5)$$
Correct answer: $$(-1,3)$$
Q4.
$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=\text{f}(3x)$$?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q5.
$$\text{f}(x)=\text{cos}(x)$$. Which points will be on the graph $$y=\text{f}(10x)$$?
An image in a quiz
Correct answer: $$(0,1)$$
$$(0,10)$$
Correct answer: $$(36,1)$$
$$(360,10)$$
$$(360,0.1)$$
Q6.
$$\text{f}(x)=\text{cos}(x)$$. 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 $$1$$?
An image in a quiz
Correct Answer: 11