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

The domain of a function is the set of values that the mapping is performed on.

The range of a function is the set of values mapped to by the function and the stated domain.

An inverse function reverses the mapping of the original function.

Checking and securing understanding of function notation

Maths

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

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

If $$\text{f}(x)= 4(x-2)$$, which is the correct notation for the inverse function $$\text{f}$$ inverse of $$x$$ ?

If $$\text{g}(4) = 6$$, then $$\text{g}^{-1}(6) =$${{}}.

If $$\text{f}(x)= 3x - 5$$, $$\text{g}(x)= 10-2x$$ and $$\text{h}(x)= x^2 + 3$$. Match up these functions with their outputs. 

Which is the correct range for $$\text{f}(x)= x^2 + 4$$ with the domain {$$x$$ : $$x$$ is any value}?

{$$\text{f}(x) : 0 \le \text{f}(x) \le 0$$}

{$$\text{f}(x) : 0 \le \text{f}(x) \le 1$$}

{$$\text{f}(x) : -1 \le \text{f}(x) \le 1$$}

{$$\text{f}(x) : -1 \le \text{f}(x)\le 0$$}

Which is the correct range for $$\text{f}(x)= \text{sin}(x)$$ with the domain {$$x : 0 \le x \le 180$$}?

$$\text{f}(x)= \frac{24}{x}$$ when {$$x : x > 0$$}

$$\text{f}(x)= \frac{24}{x}$$ when {$$x : x \ge 0$$}

$$\text{f}(x)= \frac{24}{x}$$ when {$$x : x < 0$$}

$$\text{f}(x)= \frac{24}{x}$$ when {$$x : x \le 0$$}

$$\text{f}(x)= \frac{24}{x}$$ when {$$x : x  \not= 0$$}

Which domain restrictions would make $$\text{f}(x)= \frac{24}{x}$$ a valid function?

When graphing the linear equation $$y=6x-10$$, what is the value of the $$y$$ coordinate when $$x=3$$?

When graphing the linear equation $$y=6x-10$$, what is the value of the $$y$$ coordinate when $$x=-1$$?

the set of values for a function that the mapping is performed on

a relationship which uniquely maps values in one set to another

a relationship which reverses the mapping of the original function

the set of values mapped to, by the function

Match these key words to their definitions.

When we graph the equation $$y= x^2$$, what is the minimum value (i.e. the smallest value of the $$y$$ coordinate)?

Which of these is not a valid input for $$x$$ in the equation $$y = \frac{1}{2x}$$ ?

Starter Quiz

When graphing the linear equation $$y=6x-10$$, what is the value of the $$y$$ coordinate when $$x=3$$?