A function is a mathematical relationship that uniquely maps values of one set to the values of another set.

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

Transforming graphs: y = f(x + a)

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)

Transforming graphs: y = f(−x)

Transforming graphs: y = af(x)

Transforming graphs: y = f(ax)

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

$$\text{f}(x+a)$$ is a transformation by __________.

$$\text{f}(x+a)$$ is a transformation by translation of __________.

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

$$y=\text{f}(x)$$ is graphed here. Which coordinate pairs will be on the transformation $$y=\text{f}(x+6)$$?

$$y=\text{f}(x)$$ is graphed. What transformation can we see graphed? $$y=$${{}}

$$y=\text{f}(x)$$ is graphed here. Which could the graph of the transformation be?

$$\text{f}(x)+a$$ is a {{}} of the graph of $$\text{f}(x)$$.

The output of $$\text{f}(x)$$ has $$4$$ added to it.

The input has $$4$$ added to it before the function is applied.

The output of $$\text{f}(x)$$ is multiplied by $$4$$

The output of $$\text{f}(x)$$ has $$4$$ subtracted from it.

The input has $$4$$ subtracted before the function is applied.

Match each piece of function notation to a description.

vector $$\begin{pmatrix}8 \\ 3\end{pmatrix}$$

vector $$\begin{pmatrix}3 \\ 8\end{pmatrix}$$

Shape 'a' has been transformed to shape 'b' by translation of __________.

translation by $$7$$ in the positive $$x$$-direction.

translation by $$7$$ in the negative $$x$$-direction.

translation by $$7$$ in the negative $$y$$-direction.

translation by vector $$\begin{pmatrix}-7 \\ 0\end{pmatrix}$$

The transformation of the point $$(3,-2)$$ to the position $$(-4,-2)$$ could be described by __________.

The point $$(-1,13)$$ is translated $$+8$$ in the $$x$$-direction. What is its new position?

The point $$(c,-d)$$ is translated by $$9$$ in the negative $$x$$-direction. What is its new position?

Starter Quiz

$$\text{f}(x)+a$$ is a of the graph of $$\text{f}(x)$$.