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Year 11
Higher

Transforming graphs: y = af(x)

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

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New
New
Year 11
Higher

Transforming graphs: y = af(x)

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

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Share activities with pupils
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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 a in the y-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. 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.

Visually showing pupils $$y=a$$f$$(x)$$ using graphing technology demonstrates that it is a stretch in the $$y$$-direction. Showing pupils the comparison of two tables of values explains why this occurs.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), 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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Starter quiz

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6 Questions

Q1.
$$\text{f}(x)+a$$ is a transformation of the graph of $$\text{f}(x)$$ by...
reflection
rotation
Correct answer: translation
enargement
Q2.
Match each piece of function notation to a description.
Correct Answer:$$\text{f}(x)+2$$,The output of $$\text{f}(x)$$ has $$2$$ added to it.

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

Correct Answer:$$\text{f}(x+2)$$,The input has $$2$$ added to it before the function is applied.

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

Correct Answer:$$-\text{f}(x)$$,The output of $$\text{f}(x)$$ is multiplied by $$-1$$.

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

Correct Answer:$$\text{f}(-x)$$,The input is multiplied by $$-1$$ before the function is applied.

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

Correct Answer:$$2\text{f}(x)$$,The output of $$\text{f}(x)$$ is multiplied by $$2$$.

The output of $$\text{f}(x)$$ is multiplied by $$2$$.

Q3.
Shape 'b' is an enlargement by a scale factor of of shape 'a'.
An image in a quiz
Correct Answer: 4, four
Q4.
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?
An image in a quiz
$$(2,2)$$
$$(8,2)$$
Correct answer: $$(8,0)$$
Correct answer: $$(8,4)$$
$$(6,0)$$
Q5.
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?
An image in a quiz
$$(0,5)$$
$$(15,0)$$
Correct answer: $$(0,15)$$
$$(35,0)$$
Correct answer: $$(0,35)$$
Q6.
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 $$(x,y)$$
An image in a quiz
Correct Answer: (-3, -16), (-3,-16)

Exit quiz

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6 Questions

Q1.
$$y=a\text{f}(x)$$ will transform $$y=\text{f}(x)$$ by __________ in the $$y$$-direction.
translation
rotation
reflection
Correct answer: a stretch
Q2.
The transformation $$a\text{f}(x)$$ is a stretch of $$\text{f}(x)$$ in the $$y$$-direction by a scale factor of .
Correct Answer: a
Q3.
$$y=\text{f}(x)$$ is graphed here. Which coordinate pairs will be on the graph of $$y=2\text{f}(x)$$?
An image in a quiz
$$(0,-4)$$
Correct answer: $$(0,-8)$$
Correct answer: $$(2,0)$$
$$(1,0)$$
Correct answer: $$(3,4)$$
Q4.
$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=2\text{f}(x)$$?
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 are invariant after the transformation $$y=4\text{f}(x)$$?
An image in a quiz
$$(0,1)$$
Correct answer: $$(90,0)$$
$$(180,-1)$$
Correct answer: $$(270,0)$$
$$(360,4)$$
Q6.
$$(24,40)$$ 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 $$(x,y)$$.
Correct Answer: (24, 5), (24,5)