Transforming graphs: combinations of transformations
I can recognise the effect of applying a combination of transformations to a function.
Transforming graphs: combinations of transformations
I can recognise the effect of applying a combination of transformations to a function.
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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 order of transformations is defined by the priority of operations
Keywords
Transformation - A transformation is a process that may change the size, orientation or position of a shape or graph.
Common misconception
For the combined transformation $$3$$f$$(x-2)$$ order does not matter so pupils may assume that order never matters.
For $$3$$f$$(x-2)$$ the $$3$$ affects the output, the $$y$$ value, and the $$-2$$ affects the input, the $$x$$ value. Model to show that these can happen in either order. Then point out that $$3$$f$$(x)-2$$ is two effects on the output.
To help you plan your year 11 maths lesson on: Transforming graphs: combinations of transformations, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Transforming graphs: combinations of transformations, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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Explore more key stage 4 maths lessons from the Transformations of graphs unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
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Lesson video
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Starter quiz
6 Questions
$$y=\text{f}(x)+a$$ -
Translation by $$a$$ in the $$y$$-direction.
$$y=\text{f}(x+a)$$ -
Translation by $$-a$$ in the $$x$$-direction.
$$y=-\text{f}(x)$$ -
Reflection in the $$x$$-axis.
$$y=\text{f}(-x)$$ -
Reflection in the $$y$$-axis.
$$y={a}\text{f}(x)$$ -
Stretch by scale factor $$a$$ in the $$y$$-direction.
$$y=\text{f}(ax)$$ -
Stretch by scale factor $$1\over{a}$$ in the $$x$$-direction.
$$2\text{f}(x)+3$$ -
Output of $$\text{f}(x)$$ is multiplied by $$2$$ then $$3$$ is added.
$$3\text{f}(x)+2$$ -
Output of $$\text{f}(x)$$ is multiplied by $$3$$ then $$2$$ is added.
$$3\text{f}(x+2)$$ -
Input has $$2$$ added before output is multiplied by $$3$$
$$2\text{f}(x+3)$$ -
Input has $$3$$ added before output is multiplied by $$2$$
$$2\text{f}(3x)$$ -
Input is multiplied by $$3$$ before output is multiplied by $$2$$
$$-2\text{f}(x)$$ -
Output of $$\text{f}(x)$$ is multiplied by $$-2$$
Exit quiz
6 Questions
