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...

$$\text{f}(x)+a$$ translates the graph by $$a$$ in the... 

$$y=\text{f}(x)$$ is graphed here. The second line represents what transformation of $$y=\text{f}(x)$$?

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

The points $$(-2, 24), (-1,-1), (0, 8)$$ lie on the graph of $$\text{f}(x)$$. Which points will lie on the graph of $$y=\text{f}(x)+12$$?

$$(-c,d)$$ is on the graph of $$y=\text{f}(x)$$. What will the position of this point be if the graph is transformed by $$y=\text{f}(x)+a$$?

When every point of a shape moves the same distance in the same direction the transformation is called a...

The output of $$\text{f}(x)$$ has $$11$$ added to it.

The input has $$11$$ added to it before the function is applied.

The output of $$\text{f}(x)$$ is multiplied by $$11$$

The output of $$\text{f}(x)$$ has $$11$$ subtracted from it.

The input has $$11$$ subtracted before the function is applied.

Match each piece of function notation to a description.

vector $$\begin{pmatrix}4 \\ 6\end{pmatrix}$$

vector $$\begin{pmatrix}4 \\ -6\end{pmatrix}$$

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

For the function $$\text{f}(x)$$, $$\text{f}(8)=37$$,  match these transformations of the function to their values.

The point $$(4,1)$$ is translated 'up $$5$$'. What is it's new position?

The point $$(-5,-a)$$ is translated 'down $$4$$'. What is it's new position?

Transforming graphs: y = f(x) + a

Lesson outcome