Interaction: enter domain with brackets

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Alexander Holvoet 9 months, 3 weeks ago

Published this.

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Alexander Holvoet 9 months, 3 weeks ago

Created this as a copy of Domain of square root of (a-x)/(x+b) - entering interval in pieces.

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Question statement

Find the domain of the function $f(x)=\sqrt{\frac{\var{a}-x}{x+\var{b}}}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	9
b	integer	15
end_point	rational	8/15
pos_point	rational	3/5

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xxxxxxxxxx
 
random(1..15)

JME function reference

Description

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Generated value: `integer`

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Parts

Gap-fill

Gap-fill

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The domain of this function is a single interval, namely: left_bracketleft_bound,right_boundright_bracket.

Instructions on entering your answer:

You will need to fill out 4 parts of an interval:

bracket on the left: pick the correct one from the drop-down menu: [ means 'include the value that follows'; ] means 'exclude the value that follows' ;
bounding value on the left of the interval: this is either a real number or $-\infty$ , which you enter as - infinity ;
bounding value on the right of the interval: this is either a real number or $+\infty$ , which you enter as + infinity ;
bracket on the right: pick the correct one from the drop-down menu: [ means 'exclude the value that preceeds'; ] means 'include the value that preceeds'.

Do not round values, enter a fraction if necessary.

Advice

A square root is only defined for positive values, so we need to solve the inequality $g(x)=\frac{\var{a}-x}{x+\var{b}}\geq 0$ . We make a sign chart for the rational function $g$

domain is all real numbers except $\var{-b}$ ;
there is one zero at $\var{a}$ ;
there are 3 regions to consider: $x<\var{-b}$ , $\var{-b}<x<\var{a}$ and $\var{a}<x$ . By evaluating the rational function at any point of a given region, we establish that it takes negative values on the first and the third region and positive values on the second.

This results in the following sign chart:

$x$		$\var{-b}$		$\var{a}$
$g(x)$	$-$	\	$+$	0	$-$

So, the domain is given by $]\var{-b},\var{a}]$ .

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Alexander Holvoet 9 months, 3 weeks ago

Alexander Holvoet 9 months, 3 weeks ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

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Interaction: enter domain with brackets

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Alexander Holvoet 9 months, 3 weeks ago

Alexander Holvoet 9 months, 3 weeks ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`