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Checking and securing understanding of function notation

I can define and use function notation.

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Year 11

Checking and securing understanding of function notation

I can define and use function notation.

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Lesson details

Key learning points

There is a shorthand for writing a function
The notation means that the whole function does not need to be written out each time
The notation should always be defined at the start
It is possible to substitute the notation for the function it represents

Keywords

Function - A function is a mathematical relationship that uniquely maps values of one set to the values of another set.
Domain - The domain of a function is the set of values that the mapping is performed on.
Range - The range of a function is the set of values mapped to by the function and the stated domain.
Inverse function - An inverse function reverses the mapping of the original function.

Common misconception

Pupils may confuse the domain and the range.

Drawing the graph of the function and labelling the axes correctly will help pupils connect domain and range.

If pupils are struggling to know whether a relationship is a valid function, encourage them to draw the graph as the visual representation can help.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
When graphing the linear equation $$y=6x-10$$, what is the value of the $$y$$ coordinate when $$x=3$$?

Correct Answer: 8, y=8

Q2.
When graphing the linear equation $$y=6x-10$$, what is the value of the $$y$$ coordinate when $$x=-1$$?

Correct Answer: -16

Q3.
Match these key words to their definitions.

Correct Answer:domain,the set of values for a function that the mapping is performed on

Correct Answer:function,a relationship which uniquely maps values in one set to another

Correct Answer:inverse function ,a relationship which reverses the mapping of the original function

Correct Answer:range,the set of values mapped to, by the function

Q4.
When we graph the equation $$y= x^2$$, what is the minimum value (i.e. the smallest value of the $$y$$ coordinate)?

Correct Answer: 0, y=0

Q5.
Which of these is not a valid input for $$x$$ in the equation $$y = \frac{1}{2x}$$ ?

-2

-1

Correct answer: 0

Q6.
What does $$\text{sin}^{-1} (x)$$ mean?

"sine of -1"

"sine multiplied by -1"

"1 divided by $$\text{sin}(x)$$"

Correct answer: "sine inverse of $$x$$"

"$$\text{sin}(x)$$ to the power of -1"

Assessment exit quiz

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6 Questions

Q1.
If $$\text{f}(x)= 4(x-2)$$, which is the correct notation for the inverse function $$\text{f}$$ inverse of $$x$$ ?

$$\text{f}(-1)= \frac{x}{4} + 2$$

$$-\text{f}(x)= \frac{x}{4} + 2$$

Correct answer: $$\text{f}^{-1}(x)= \frac{x}{4} + 2$$

$$\text{f}(x)^{-1}= \frac{x}{4} + 2$$

Q2.
If $$\text{g}(4) = 6$$, then $$\text{g}^{-1}(6) =$$ .

Correct Answer: 4

Q3.
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.

Correct Answer:$$\text{f}(-2)$$,$$-11$$

Correct Answer:$$\text{g}(-2)$$,$$14$$

Correct Answer:$$\text{h}(-2)$$,$$7$$

Correct Answer:$$\text{f}(1)$$,$$-2$$

Correct Answer:$$\text{g}(1)$$,$$8$$

Correct Answer:$$\text{h}(1)$$,$$4$$

Q4.
Which is the correct range for $$\text{f}(x)= x^2 + 4$$ with the domain {$$x$$ : $$x$$ is any value}?

{$$\text{f}(x) : \text{f}(x) > 4$$}

Correct answer: {$$\text{f}(x) : \text{f}(x) \ge 4$$}

{$$\text{f}(x) : \text{f}(x) < 4$$}

{$$\text{f}(x) : \text{f}(x) \le 4$$}

Q5.
Which is the correct range for $$\text{f}(x)= \text{sin}(x)$$ with the domain {$$x : 0 \le x \le 180$$}?

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

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

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

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

Q6.
Which domain restrictions would make $$\text{f}(x)= \frac{24}{x}$$ a valid function?

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

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

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

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

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

Lesson appears in

UnitMaths / Transformations of graphs

Maths

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Checking and securing understanding of function notation

Checking and securing understanding of function notation

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.When graphing the linear equation $$y=6x-10$$, what is the value of the $$y$$ coordinate when $$x=3$$?

Q2.When graphing the linear equation $$y=6x-10$$, what is the value of the $$y$$ coordinate when $$x=-1$$?

Q3.Match these key words to their definitions.

Q4.When we graph the equation $$y= x^2$$, what is the minimum value (i.e. the smallest value of the $$y$$ coordinate)?

Q5.Which of these is not a valid input for $$x$$ in the equation $$y = \frac{1}{2x}$$ ?

Q6.What does $$\text{sin}^{-1} (x)$$ mean?

Assessment exit quiz

6 Questions

Q1.If $$\text{f}(x)= 4(x-2)$$, which is the correct notation for the inverse function $$\text{f}$$ inverse of $$x$$ ?

Q2.If $$\text{g}(4) = 6$$, then $$\text{g}^{-1}(6) =$$ .

Q3.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.

Q4.Which is the correct range for $$\text{f}(x)= x^2 + 4$$ with the domain {$$x$$ : $$x$$ is any value}?

Q5.Which is the correct range for $$\text{f}(x)= \text{sin}(x)$$ with the domain {$$x : 0 \le x \le 180$$}?

Q6.Which domain restrictions would make $$\text{f}(x)= \frac{24}{x}$$ a valid function?

Lesson appears in

UnitMaths / Transformations of graphs

Maths

Q1.
When graphing the linear equation $$y=6x-10$$, what is the value of the $$y$$ coordinate when $$x=3$$?

Q2.
When graphing the linear equation $$y=6x-10$$, what is the value of the $$y$$ coordinate when $$x=-1$$?

Q3.
Match these key words to their definitions.

Q4.
When we graph the equation $$y= x^2$$, what is the minimum value (i.e. the smallest value of the $$y$$ coordinate)?

Q5.
Which of these is not a valid input for $$x$$ in the equation $$y = \frac{1}{2x}$$ ?

Q6.
What does $$\text{sin}^{-1} (x)$$ mean?

Q1.
If $$\text{f}(x)= 4(x-2)$$, which is the correct notation for the inverse function $$\text{f}$$ inverse of $$x$$ ?

Q2.
If $$\text{g}(4) = 6$$, then $$\text{g}^{-1}(6) =$$ .

Q3.
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.

Q4.
Which is the correct range for $$\text{f}(x)= x^2 + 4$$ with the domain {$$x$$ : $$x$$ is any value}?

Q5.
Which is the correct range for $$\text{f}(x)= \text{sin}(x)$$ with the domain {$$x : 0 \le x \le 180$$}?

Q6.
Which domain restrictions would make $$\text{f}(x)= \frac{24}{x}$$ a valid function?