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.
These resources will be removed by end of Summer Term 2025.
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.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
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.
Licence
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
