Transforming graphs: y = f(ax)
I can recognise the effect of applying the transformation y = f(ax) to a graph.
- Year 11
Transforming graphs: y = f(ax)
I can recognise the effect of applying the transformation y = f(ax) 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 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?
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.$$a\text{f}(x)$$ is a transformation of the graph of $$\text{f}(x)$$ by a __________ in the $$y$$-direction.
Q2.Match each piece of function notation to a description.
$$\text{f}(x)+15$$ -Â The output of $$\text{f}(x)$$ has $$15$$ added to it.
$$\text{f}(x+15)$$ -Â The input has $$15$$ added to it before the function is applied.
$$15\text{f}(x)$$ -Â The output of $$\text{f}(x)$$ is multiplied by $$15$$.
$$\text{f}(15x)$$ -Â The input is multiplied by $$15$$ before the function is applied
Q3.Shape 'b' is an enlargement of shape 'a' by scale factor of...
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?
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?
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?
Assessment exit quiz
6 Questions
Q1.$$y=\text{f}(ax)$$ will transform $$y=\text{f}(x)$$ by stretch in the -direction.
Q2.The transformation $$\text{f}(ax)$$ is a stretch of $$\text{f}(x)$$ in the $$x$$-direction by a of $$1\over{a}$$.
Q3.$$y=\text{f}(x)$$ is graphed here. Which coordinate pairs will be on the graph $$y=\text{f}(4x)$$?
Q4.$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=\text{f}(3x)$$?
Q5.$$\text{f}(x)=\text{cos}(x)$$. Which points will be on the graph $$y=\text{f}(10x)$$?
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 $$1$$?
