Transforming graphs: y = af(x)
I can recognise the effect of applying the transformation y = af(x) to a graph.
- Year 11
Transforming graphs: y = af(x)
I can recognise the effect of applying the transformation y = af(x) to a graph.
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 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.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.$$\text{f}(x)+a$$ is a transformation of the graph of $$\text{f}(x)$$ by...
Q2.Match each piece of function notation to a description.
$$\text{f}(x)+2$$ -Â The output of $$\text{f}(x)$$ has $$2$$ added to it.
$$\text{f}(x+2)$$ -Â The input has $$2$$ added to it before the function is applied.
$$-\text{f}(x)$$ -Â The output of $$\text{f}(x)$$ is multiplied by $$-1$$.
$$\text{f}(-x)$$ -Â The input is multiplied by $$-1$$ before the function is applied.
$$2\text{f}(x)$$ -Â The output of $$\text{f}(x)$$ is multiplied by $$2$$.
Q3.Shape 'b' is an enlargement by a scale factor of of shape 'a'.
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?
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?
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 $$(x,y)$$
Assessment exit quiz
6 Questions
Q1.$$y=a\text{f}(x)$$ will transform $$y=\text{f}(x)$$ by __________ in the $$y$$-direction.
Q2.The transformation $$a\text{f}(x)$$ is a stretch of $$\text{f}(x)$$ in the $$y$$-direction by a scale factor of .
Q3.$$y=\text{f}(x)$$ is graphed here. Which coordinate pairs will be on the graph of $$y=2\text{f}(x)$$?
Q4.$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=2\text{f}(x)$$?
Q5.$$\text{f}(x)=\text{cos}(x)$$ Which points are invariant after the transformation $$y=4\text{f}(x)$$?
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 $$(x,y)$$.
