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Year 11
Higher

Checking and securing understanding of moving between function notation and the definition

I can fluently move between function notation and the function it represents, including when the function has been altered.

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Year 11
Higher

Checking and securing understanding of moving between function notation and the definition

I can fluently move between function notation and the function it represents, including when the function has been altered.

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Share activities with pupils
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Lesson details

Key learning points

  1. Changing the function changes what it represents
  2. The change in notation can be seen in the algebraic form of the function it represents
  3. If a specific linear function is considered, the effects of this can be seen clearly

Keywords

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

Common misconception

A common error is to not substitute into all variable terms where there is more than one in a function. For example, 'Write a simplified expression for f$$(x+3)$$ when f$$(x)=x^2-4x$$'

Use brackets when substituting. For example, for 'Write a simplified expression for f$$(x+3)$$ when f$$(x)=x^2-4x$$' you would write f$$(x+3)=(x+3)^2-4(x+3)$$

Mini-whiteboards are a really useful resource for this lesson. When 'Checking for understanding' if pupils write their answers on mini-whiteboards you can quickly spot any common errors quickly and provide timely intervention.
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 uniquely maps values from the domain to values in the range.
Correct Answer: function
Q2.
If $$\text{f}(x)= 5x-4$$ what is the value of $$\text{f}(3)$$ ?
Correct Answer: 11
Q3.
If $$\text{g}(x)= x^2- 3x$$ what is the value of $$\text{g}(4)$$ ?
Correct Answer: 4
Q4.
Expand and simplify $$(x+3)^2$$.
$$x^2+9$$
$$x^2 + 3x + 6$$
$$x^2 + 3x + 9$$
Correct answer: $$x^2 + 6x + 9$$
Q5.
Simplify $$3(4(2x+1)-5)$$.
$$24x-64$$
$$24x-48$$
Correct answer: $$24x-3$$
$$24x+7$$
Q6.
If $$\text{f}(x) = 2x + 4$$ and $$\text{g}(x) = 3x- 2$$, what is an expression for $$\text{fg}(x)$$ ?
$$5x+2$$
Correct answer: $$6x$$
$$6x-8$$
$$6x+ 10$$

Exit quiz

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6 Questions

Q1.
Match up these manipulations of $$\text{f}(x)$$ to their definitions.
Correct Answer:$$\text{f}(x+3)$$,Add 3 to the given value of $$x$$ then substitute into the function.

Add 3 to the given value of $$x$$ then substitute into the function.

Correct Answer:$$\text{f}(x)+3$$,Evaluate the function for the given value of $$x$$ then add 3

Evaluate the function for the given value of $$x$$ then add 3

Correct Answer:$$\text{f}(3x)$$,Multiply $$x$$ by 3 then substitute this value into the function

Multiply $$x$$ by 3 then substitute this value into the function

Correct Answer:$$3\text{f}(x)$$,Evaluate the function for the given value of $$x$$ then multiply by 3

Evaluate the function for the given value of $$x$$ then multiply by 3

Q2.
If $$\text{g}(x)=3x-5$$ match up these manipulation to their value when $$x=3$$.
Correct Answer:$$\text{g}(x+2)$$,$$10$$

$$10$$

Correct Answer:$$\text{g}(x) + 2$$,$$6$$

$$6$$

Correct Answer:$$\text{g}(2x)$$,$$13$$

$$13$$

Correct Answer:$$2\text{g}(x)$$,$$8$$

$$8$$

Q3.
When $$\text{f}(x)=2x+4$$ which of these is an expression for $$\text{f}(x+3)$$?
$$2x+7$$
Correct answer: $$2x+10$$
$$2x+12$$
$$5x+4$$
$$5x+7$$
Q4.
When $$\text{f}(x)=x^2+4x$$ which of these is an expression for $$2\text{f}(x)$$?
$$2x^2 + 4x$$
Correct answer: $$2x^2 + 8x$$
$$4x^2 + 4x$$
$$4x^2 + 8x$$
Q5.
When $$\text{f}(x)=5-3x$$ which of these is an expression for $$2\text{f}(x-4)$$?
$$-6x-14$$
$$2-6x$$
$$17-6x$$
Correct answer: $$34-6x$$
Q6.
When $$\text{f}(x)=2x-x^2$$ which of these is an expression for $$\text{f}(3x)-2$$?
$$5x-x^2-2$$
$$5x-9x^2-2$$
$$6x-x^2-2$$
$$6x-3x^2-2$$
Correct answer: $$6x-9x^2-2$$