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

Problem solving with graph transformations

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: y = f(ax)

Transforming graphs: combinations of 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

The graph of $$y=x^2$$ has been transformed to get a new graph. What is the equation of this new graph?

The graph of $$y=x^2-2x$$ has been transformed to get a new graph. What is the equation of this new graph?

The graph of $$\text{f}(x)=2^x + 1$$ has an asymptote at $$y=1$$. Match up the transformations with the equation of the asymptote after the transformation.

The graph of $$\text{f}(x)= \text{tan}(x)$$ where $$-90 \le x \le 90$$ has asymptotes at $$x=-90$$ and $$x=90$$, which of these transformations will not change the position of the asymptotes ? 

Translation of 5 in the positive $$y$$ direction

Translation of 5 in the negative $$x$$ direction

Stretch of $$1 \over 5$$ in the $$x$$ direction

Match the transformed functions of $$ \text {f}(x)$$ to their descriptions. 

The graph of $$y= \text{f}(x)$$ is labelled. What other function of $$x$$ has been graphed?

The graph of $$y= \text{g} (x)$$ is labelled. What other function of $$x$$ has been graphed?

An __________ is a line which a curve approaches but never touches.

Which of these is equivalent to $$x^2 - 4x + 6$$?

Starter Quiz

Match the transformed functions of $$ \text {f}(x)$$ to their descriptions.