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

Transforming graphs: y = af(x)

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 = 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

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

The transformation $$a\text{f}(x)$$ is a stretch of $$\text{f}(x)$$ in the $$y$$-direction by a scale factor of {{}}.

$$y=\text{f}(x)$$ is graphed here. Which coordinate pairs will be on the graph of $$y=2\text{f}(x)$$?

$$y=\text{f}(x)$$ is graphed. Which of these images shows the transformation $$y=2\text{f}(x)$$?

$$\text{f}(x)=\text{cos}(x)$$ Which points are invariant after the transformation $$y=4\text{f}(x)$$?

$$(24,40)$$ is a point on the line $$y=8\text{f}(x)$$. What was the position of this point on the line $$y=\text{f}(x)$$ before the transformation? Give your answer in the form $$(x,y)$$.

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

The output of $$\text{f}(x)$$ has $$2$$ added to it.

The input has $$2$$ added to it before the function is applied.

The output of $$\text{f}(x)$$ is multiplied by $$-1$$.

The input is multiplied by $$-1$$ before the function is applied.

The output of $$\text{f}(x)$$ is multiplied by $$2$$.

Match each piece of function notation to a description.

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

Shape 'a' is enlarged by scale factor $$2$$ from centre of enlargement $$(0,0)$$. Which of these coordinate pairs will be vertices of the enlargement?

Shape 'a' is enlarged by scale factor $$5$$ from centre of enlargement $$(0,0)$$. Which of these coordinate pairs will be vertices of the enlargement?

Shape 'a' is enlarged by scale factor $$8$$ from centre of enlargement $$(-3,0)$$. What will the new position of the marked vertice be? Give your answer in the form $$(x,y)$$ {{}}

Starter Quiz

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