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

Transforming graphs: combinations of transformations

Maths

Checking and securing understanding of function notation

Checking and securing understanding of moving between function notation and the definition

Transforming graphs: y = f(x) + a

Transforming graphs: y = f(x + a)

Transforming graphs: y = −f(x)

Transforming graphs: y = f(−x)

Transforming graphs: y = af(x)

Transforming graphs: y = f(ax)

Problem solving with graph transformations

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. 

In this unit pupils learn how to perform transformations on functions both algebraically and visually.

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 $$y=-\text{f}(x)$$?

Transforming graphs: combinations of transformations

Lesson outcome