CA7 Composite functions

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From users who are members of Skills Audits for Maths and Stats :

Lauren Desoysa	said	Ready to use	1 year, 1 month ago
Megan Oliver	said	Needs to be tested	1 year, 1 month ago

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Will Morgan 11 months, 3 weeks ago

Published this.

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Lauren Desoysa 1 year, 1 month ago

Gave some feedback: Ready to use

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Megan Oliver 1 year, 1 month ago

Gave some feedback: Needs to be tested

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Megan Oliver 1 year, 1 month ago

Created this as a copy of Functions: Composite Functions 1.

Name	Status	Author	Last Modified
Functions: Evaluating Functions 2	Ready to use	Ben McGovern	10/10/2022 13:02
Functions: Evaluating Functions 3	Ready to use	Ben McGovern	10/10/2022 13:02
Functions: Composite Functions 1	Ready to use	Ben McGovern	10/10/2022 13:00
Functions: Composite Functions 2	Ready to use	Ben McGovern	10/10/2022 13:00
Functions: Composite Functions 3a	Ready to use	Ben McGovern	10/10/2022 13:00
Functions: Composite Functions 3b	Ready to use	Ben McGovern	24/04/2023 14:32
Functions: Composite Functions 4a	Ready to use	Ben McGovern	10/10/2022 13:00
Functions: Composite Functions 4b	Ready to use	Ben McGovern	10/10/2022 13:00
Functions: Evaluating Composite Functions 1 - Modulus Functions	Ready to use	Ben McGovern	10/10/2022 13:02
Functions: Composite Functions 5 - Modulus Functions	Ready to use	Ben McGovern	10/10/2022 13:01
CA7 Composite functions	Ready to use	Megan Oliver	09/04/2024 15:42

There are 18 other versions that do you not have access to.

Question statement

If $f(x)=\simplify{{m}x+{c}}$ and $g(x)=\simplify{{n}x+{d}}$ , find expressions for $f\circ g(x)$ and $g \circ f(x)$ .

Recall: $f \circ g(x) \equiv f(g(x))$ and $g \circ f(x) \equiv g(f(x))$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

n	integer	2
m	integer	5
c	integer	-3
d	integer	-2

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Value

xxxxxxxxxx
 
random(2..5)

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Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

Statement
Advice
"Unnamed part" → "Gap 0" - Correct answer
"Unnamed part" → "Gap 1." - Correct answer

Parts

Gap-fill
1. Gap Gap 0 Mathematical expression
  Add
2. Gap Gap 1. Mathematical expression
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$f \circ g(x)=$ Gap 0

$g \circ f(x)=$ Gap 1.

Advice

To find the composition $f \circ g(x)$ we are substituting the expression for $g(x)$ into the function $f(x)$ , replacing the $x$ -terms with the function $g(x)$ . Similarly, to find the composition $g \circ f(x)$ we are substituting the expression for $f(x)$ into the function $g(x)$ , replacing the $x$ -terms with the function $f(x)$ .

So, for $f(x)=\simplify{{m}x+{c}}$ and $g(x)=\simplify{{n}x+{d}}$ ,

$\begin{split} f \circ g(x) \equiv f(g(x)) &\,= \simplify{{m}({n}x+{d})+{c}} \\ &\,=\simplify[!collectNumbers,unitFactor]{{m*n}x+{m*d}+{c}} \\ &\,=\simplify{{m*n}x+{m*d+c}}, \end{split}$

and

$\begin{split} g \circ f(x) \equiv g(f(x)) &\,= \simplify{{n}({m}x+{c})+{d}} \\ &\,=\simplify[!collectNumbers,unitFactor]{{m*n}x+{n*c}+{d}} \\ &\,=\simplify{{m*n}x+{n*c+d}}. \end{split}$

Use this link to find resources to help you revise how to find composite functions.

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Will Morgan 11 months, 3 weeks ago

Lauren Desoysa 1 year, 1 month ago

Megan Oliver 1 year, 1 month ago

Megan Oliver 1 year, 1 month ago

Error in variable testing condition

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Generated value: `integer`

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CA7 Composite functions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Will Morgan 11 months, 3 weeks ago

Lauren Desoysa 1 year, 1 month ago

Megan Oliver 1 year, 1 month ago

Megan Oliver 1 year, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`