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Year 11
Higher

Defining function notation

I can define function notation.

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New
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Year 11
Higher

Defining function notation

I can define function notation.

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Lesson details

Key learning points

  1. There is a shorthand for writing a function.
  2. The notation means that the whole function does not need to be written out each time.
  3. The notation should always be defined at the start.
  4. 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.

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 (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
A function is a mathematical relationship that uniquely __________ values of one set to the values of another set.
Correct answer: maps
transfers
substitutes
ages
Q2.
Match the expression to the description of each function.
Correct Answer:$$3x+7$$,$$x$$ is multiplied by $$3$$ then $$7$$ is added.

$$x$$ is multiplied by $$3$$ then $$7$$ is added.

Correct Answer:$$3(x+7)$$,$$7$$ is added to $$x$$ then the sum is multiplied by $$3$$

$$7$$ is added to $$x$$ then the sum is multiplied by $$3$$

Correct Answer:$$3x-7$$,$$x$$ is multiplied by $$3$$ then $$7$$ subtracted

$$x$$ is multiplied by $$3$$ then $$7$$ subtracted

Correct Answer:$$7-3x$$,$$x$$ is multiplied by $$3$$ then subtracted from $$7$$

$$x$$ is multiplied by $$3$$ then subtracted from $$7$$

Correct Answer:$$7(3-x)$$,$$x$$ is subtracted from $$3$$, then the result is multiplied by $$7$$

$$x$$ is subtracted from $$3$$, then the result is multiplied by $$7$$

Correct Answer:$$7(x-3)$$,$$3$$ is subtracted from $$x$$, then the result is multiplied by $$7$$

$$3$$ is subtracted from $$x$$, then the result is multiplied by $$7$$

Q3.
When graphing the linear equation $$y=7x+9$$ what is the value of the $$y$$ coordinate when $$x=5$$?
Correct Answer: 44, y=44
Q4.
When graphing the linear equation $$y=7x+9$$ what is the value of the $$y$$ coordinate when $$x=-5$$?
$$44$$
$$26$$
Correct answer: $$-26$$
$$-44$$
Q5.
When graphing the equation $$y=10-x^2$$ what is the value of the $$y$$ coordinate when $$x=-3$$?
$$19$$
Correct answer: $$1$$
$$-1$$
$$-19$$
$$-13$$
Q6.
Which of the below are invalid inputs into the equation $$6\over{x^2+x-20}$$?
$$x=20$$
$$x=0$$
$$x=-1$$
Correct answer: $$x=4$$
Correct answer: $$x=-5$$

Exit quiz

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6 Questions

Q1.
The __________ of a function is the set of values mapped to by the function and the stated domain.
output
Correct answer: range
domain
input
Q2.
Instead of writing 'the function $$5x-8$$' we would write it using the shorthand notation ...
$$5{\text{f}}(x)-8$$
$${\text{f}}=5x-8$$
$${\text{f}}x=5x-8$$
Correct answer: $${\text{f}}(x)=5x-8$$
$${\text{f}}(x)+5x-8$$
Q3.
If $${\text{f}}(x)=12-5x$$ then $${\text{f}}(3)=$$ .
Correct Answer: -3
Q4.
If $${\text{f}}(x)=12-5x$$ evaluate $${\text{f}}(-2)$$.
Correct answer: $$22$$
$$2$$
$$-2$$
$$-22$$
Q5.
If $${\text{f}}(x)=5x+12$$ evaluate $$7{\text{f}}(4)$$
Correct Answer: 224, 7f(4)=224
Q6.
If $${\text{f}}(x)=5x+12$$ and $${\text{g}}(x)=2-3x$$ evaluate $${\text{f}}(4)-{\text{g}}(3)$$
Correct Answer: 39, f(4)-g(3)=39