Maria's copy of Domain of a square root function

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Maria Aneiros

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Needs to be tested

5 years, 2 months ago

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Maria Aneiros 5 years, 2 months ago

Gave some feedback: Needs to be tested

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Maria Aneiros 5 years, 10 months ago

Created this as a copy of Domain of a square root function.

Name	Status	Author	Last Modified
Domain of a polynomial	Ready to use	Ben Brawn	19/10/2023 02:28
Domain of a rational function	Ready to use	Ben Brawn	09/10/2023 11:15
Domain of an exponential	Ready to use	Ben Brawn	08/04/2025 10:05
Domain of a log function	Ready to use	Ben Brawn	09/10/2023 11:17
Domain of a piecewise function	Ready to use	Ben Brawn	12/10/2023 02:17
Domain of a square root function	Ready to use	Ben Brawn	04/10/2024 05:33
Domain of a trigonometric function (radians)	Has some problems	Ben Brawn	18/10/2024 00:24
Domain of a trigonometric function (degrees)	Ready to use	Ben Brawn	16/06/2017 06:05
Quadratic Inequalities	Ready to use	Ben Brawn	22/06/2017 07:24
Quadratic Inequalities 2	Ready to use	Ben Brawn	22/06/2017 07:17
Luis's copy of Quadratic Inequalities 2	draft	Luis Hernandez	17/01/2019 19:16
Kaye's copy of Quadratic Inequalities	Ready to use	Kaye Guan	18/01/2019 00:26
Joshua's copy of Domain of a piecewise function	draft	Joshua Calcutt	02/04/2019 02:05
Function Quiz Q5	draft	Joshua Calcutt	02/04/2019 07:31
Terry's copy of Quadratic Inequalities	draft	Terry Young	03/04/2019 17:33
Terry's copy of Quadratic Inequalities 2	draft	Terry Young	03/04/2019 17:34
Function Quiz Q5 function defined by { #2 (three parts)	draft	Joshua Calcutt	24/07/2020 07:38
Maria's copy of Function Quiz Q5	draft	Maria Aneiros	25/05/2019 07:25
Maria's copy of Domain of a square root function	Needs to be tested	Maria Aneiros	05/02/2020 06:54
Maria's copy of Domain of a rational function	Needs to be tested	Maria Aneiros	05/02/2020 06:50
Maria's copy of Domain of a polynomial	Needs to be tested	Maria Aneiros	05/02/2020 06:47
Maria's copy of Domain of a trigonometric function (degrees)	draft	Maria Aneiros	25/05/2019 07:58
Maria's copy of Domain of a trigonometric function (radians)	draft	Maria Aneiros	25/05/2019 08:00
Maria's copy of Domain of an exponential	draft	Maria Aneiros	25/05/2019 08:01
Maria's copy of Domain of a log function	draft	Maria Aneiros	05/02/2020 07:14
Quadratic Inequalities	draft	Xiaodan Leng	10/07/2019 22:39
Quadratic Inequalities	draft	Xiaodan Leng	11/07/2019 02:19
Quadratic Inequalities 2	draft	Xiaodan Leng	11/07/2019 02:19
Domain of a trigonometric function (degrees)	draft	Xiaodan Leng	11/07/2019 02:21
Domain of a trigonometric function (radians)	draft	Xiaodan Leng	11/07/2019 02:22
Domain of a square root function	draft	Xiaodan Leng	11/07/2019 02:22
Domain of a log function	draft	Xiaodan Leng	11/07/2019 02:23
Domain of a rational function	draft	Xiaodan Leng	11/07/2019 02:24
Function defined by { #1	draft	Yuri Anissimov	17/07/2020 01:20
Function defined by { #2	draft	Yuri Anissimov	20/07/2020 07:07
NC Math 3 Joshua's copy of Domain of a piecewise function	draft	Terry Young	10/02/2020 19:28
Definisjonsmengden piecewise	Ready to use	Elena Malyutina	02/09/2021 11:25
Definisjonsmengden polynom	Ready to use	Elena Malyutina	26/08/2024 14:48
Ugur's copy of Domain of a rational function	Ready to use	Ugur Efem	14/01/2022 15:06
Domain of a rational function short version	Ready to use	Ugur Efem	12/01/2022 11:44

There are 73 other versions that do you not have access to.

Question statement

Given the real functions below, you should be able to determine their domains.

Give any introductory information the student needs.

			Name	Type	Generated Value

out	expression	g
inp	expression	s
num	list	[ 3, 5 ]
n	integer	4
c	list	List of 24 items
rat	string	\[\simplify{{out}({inp})=({num
a	integer	-12
b	integer	-2
base	integer	4
d	integer	11

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
expression(random('f','h','g','p','q','y'))

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Description

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

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Generated value: `expression`

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Choose one from a list
Part c) Choose one from a list
Part d) Choose one from a list

Gap-fill

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

Give an example of a real number that is in the domain of the function

$f(x)=\sqrt{x}.$

Unnamed gap $\in \text{dom}(f)$

Advice

a) The domain of $f(x)=\sqrt{x}$ is the set of all non-negative numbers, i.e. $\{x\in\mathbb{R}:\,x\ge0\}$ or in interval notation, $[0,\infty)$ . This means that the square root of any negative number is not defined.

b) For a function such as $g(t)=\sqrt{\simplify{t-{c[0]}}}$ we require that the square root acts on a non-negative number, that is, $\simplify{t-{c[0]}>=0}$ . Rearranging this inequality for $t$ gives $\simplify{t>={c[0]}}$ . Therefore, $\text{dom}(g)=\{t\in\mathbb{R}:\,\simplify{t>={c[0]}}\}$ .

c) For a function such as $\simplify{{out}({inp})}=\sqrt{\simplify{{inp}^2-{a+b}{inp}+{a*b}}}$ we require that the square root acts on a non-negative number, that is, $\simplify{{inp}^2-{a+b}{inp}+{a*b}>=0}$ . Notice $\simplify{{inp}^2-{a+b}{inp}+{a*b}=({inp}-{a})({inp}-{b})}$ , which is non-negative when $\simplify{({inp}-{a})}$ and $\simplify{({inp}-{b})}$ are both negative, or both non-negative. That is, we require $\simplify{{inp}<={a}}$ or $\simplify{{inp}>={b}}$ . Therefore, $\text{dom}(\simplify{{out}})=\{\simplify{{inp}}\in\mathbb{R}:\,\simplify{{inp}<={a}} \text{ or } \simplify{{inp}>={b}}\}$ .

d) For a function such as $\simplify{{out}({inp})=root(-{inp}^2+{d}{inp},2)}$ we require that the square root acts on a non-negative number, that is, $\simplify{-{inp}^2+{d}{inp}>=0}$ . Notice $\simplify{-{inp}^2+{d}{inp}={inp}({d}-{inp})}$ , which is non-negative when $\simplify{{inp}}$ and $\simplify{({d}-{inp})}$ are both negative, or both non-negative. That is, we require $\simplify{0<={inp}<={d}}$ . Therefore, $\text{dom}(\simplify{{out}})=\{\simplify{{inp}}\in\mathbb{R}:\,\simplify{0<={inp}<={d}}\}$ .

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Maria's copy of Domain of a square root function

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Maria Aneiros 5 years, 2 months ago

Maria Aneiros 5 years, 10 months ago

Error in variable testing condition

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Generated value: `expression`

Parts

Gap-fill

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Maria's copy of Domain of a square root function

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Maria Aneiros 5 years, 2 months ago

Maria Aneiros 5 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: expression

Parts

Gap-fill

Generated value: `expression`