A transformation is a process that may change the size, orientation or position of a shape or graph.

Transforming graphs: combinations of transformations

Maths

In this unit, function notation is used to describe various transformations. Pupils therefore need to be familiar with function notation which is introduced in the prior unit. 

Transformations of graphs

$$-\text{f}(-x)$$ will transform $$\text{f}(x)$$ by two __________.

$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=-2\text{f}(x)$$?

$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=2\text{f}(x)+2$$?

$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=-\text{f}(x+2)$$?

$$\text{f}(x)=\text{cos}(x)$$. Where will the marked point be after the transformation $$y=3\text{f}(2x)$$?

$$\text{f}(x)=\text{cos}(x)$$. Where will the marked point be after the transformation $$y=-\text{f}\left({1\over2}x\right)+1$$? Give your answer in the form $$(x,y)$$

$$y=\text{f}(x)+a$$, $$y=\text{f}(x+a)$$, $$y={a}\text{f}(x)$$, and $$y=\text{f}(ax)$$ are all {{}} of $$y=\text{f}(x)$$.

Translation by $$a$$ in the $$y$$-direction.

Translation by $$-a$$ in the $$x$$-direction.

Stretch by scale factor $$a$$ in the $$y$$-direction.

Stretch by scale factor $$1\over{a}$$ in the $$x$$-direction.

Match the notation to its transformation.

Output of $$\text{f}(x)$$ is multiplied by $$2$$ then $$3$$ is added.

Output of $$\text{f}(x)$$ is multiplied by $$3$$ then $$2$$ is added.

Input has $$2$$ added before output is multiplied by $$3$$

Input has $$3$$ added before output is multiplied by $$2$$

Input is multiplied by $$3$$ before output is multiplied by $$2$$

Output of $$\text{f}(x)$$ is multiplied by $$-2$$

Match each piece of function notation to a description.

$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=2\text{f}(x)$$?

$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=\text{f}(x-6)$$?

$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=-\text{f}(x)$$?

This lesson will be removed by end of Summer Term 2025.

Transforming graphs: combinations of transformations

Lesson outcome

This lesson will be removed by end of Summer Term 2025.