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

Transforming graphs: y = f(ax)

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: combinations of transformations

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

$$y=\text{f}(ax)$$ will transform $$y=\text{f}(x)$$ by stretch in the {{}}-direction.

The transformation $$\text{f}(ax)$$ is a stretch of $$\text{f}(x)$$ in the $$x$$-direction by a {{}} of $$1\over{a}$$.

$$y=\text{f}(x)$$ is graphed here. Which coordinate pairs will be on the graph $$y=\text{f}(4x)$$?

$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=\text{f}(3x)$$?

$$\text{f}(x)=\text{cos}(x)$$. Which points will be on the graph $$y=\text{f}(10x)$$?

$$\text{f}(x)=\text{cos}(x)$$. 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 $$1$$?

$$a\text{f}(x)$$ is a transformation of the graph of $$\text{f}(x)$$ by a __________ in the $$y$$-direction.

The output of $$\text{f}(x)$$ has $$15$$ added to it.

The input has $$15$$ added to it before the function is applied.

The output of $$\text{f}(x)$$ is multiplied by $$15$$.

The input is multiplied by $$15$$ before the function is applied

Match each piece of function notation to a description.

Shape 'b' is an enlargement of shape 'a' by scale factor of...

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?

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? {{}}

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?

Starter Quiz

$$a\text{f}(x)$$ is a transformation of the graph of $$\text{f}(x)$$ by a __________ in the $$y$$-direction.