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

Transforming graphs: y = −f(x)

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

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

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

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

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

Here is a table of values for an unknown function $$\text{f}(x)$$ Which coordinate pairs will be on the transformed graph $$y=-\text{f}(x)$$?

$$(-c,-d)$$ is on the graph of $$y=\text{f}(x)$$, $$c\neq{0}$$ and $$d\neq{0}$$. What will be the position of this point on the graph $$y=-\text{f}(x)$$?

$$\text{f}(x)+a$$ and $$\text{f}(x+a)$$ transform the graph of $$\text{f}(x)$$ by __________.

The output of $$\text{f}(x)$$ has $$5$$ added to it.

The input has $$5$$ added to it before the function is applied.

The output of $$\text{f}(x)$$ is multiplied by $$5$$

The output of $$\text{f}(x)$$ has $$5$$ subtracted from it.

The input has $$5$$ subtracted before the function is applied.

Match each piece of function notation to a description.

translation by vector $$\begin{pmatrix}-6 \\ 0\end{pmatrix}$$

translation by vector $$\begin{pmatrix}0 \\ -6\end{pmatrix}$$

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

Translation by vector $$\begin{pmatrix}-10 \\ 0\end{pmatrix}$$

Translation by vector $$\begin{pmatrix}0 \\ 10\end{pmatrix}$$

Translation by vector $$\begin{pmatrix}0 \\ -10\end{pmatrix}$$

The transformation of the point $$(-2,5)$$ to the position $$(-2,-5)$$ could be described by __________.

The point $$(7,-9)$$ is reflected in the $$x$$-axis. What is its new position?

The point $$(-a,b)$$ is reflected in the $$x$$-axis. What is its new position?

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

Transforming graphs: y = −f(x)

Lesson outcome

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