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March 29, 2024, 07:24:39 am

Author Topic: VCE Methods Question Thread!  (Read 4802735 times)  Share 

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RuiAce

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Re: VCE Methods Question Thread!
« Reply #15795 on: December 29, 2017, 03:47:03 pm »
+1
It specified that the domain of it's inverse was [-4,0]

So it is still one-to-one.

On the other hand, if the domain were the implied domain \( [-4,4] \) then it would be many-to-one

snowisawesome

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Re: VCE Methods Question Thread!
« Reply #15796 on: December 29, 2017, 06:40:57 pm »
0
My bad - I read the question as a quadratic.

Even if there was a domain restriction, I don't think there is a way to do this in VCE methods - may I ask where the question is from?
It's in the maths quest 12 methods textbook - so definitely part of vce methods, but the question asked to sketch the graph on y = 9x-x^3 and its inverse using the CAS

Another question
if f(x) = x^2 - 10x + 25, with a domain of [a, infinity), find the smallest value of a so that f^(-1) exists
I have come across these types of questions quite a few times and don't understand how to do them. Any help would be appreciated
« Last Edit: December 29, 2017, 06:46:28 pm by snowisawesome »

Syndicate

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Re: VCE Methods Question Thread!
« Reply #15797 on: December 29, 2017, 06:46:29 pm »
0
It's in the maths quest 12 methods textbook - so definitely part of vce methods.

Another question
if f(x) = x^2 - 10x + 25, with a domain of [a, infinity), find the smallest value of a so that f^(-1) exists
I have come across these types of questions quite a few times and don't understand how to do them. Any help would be appreciated

The inverse of a function only exists, if the fuction is one-to-one Since f(x) is a quadratic, it is not a one-to-one function. Hence, you'll need to calculate the x-value of the turning point of this quadratic to find a (graphing this function would make it easier to find a).
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RuiAce

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Re: VCE Methods Question Thread!
« Reply #15798 on: December 29, 2017, 06:50:13 pm »
0
It's in the maths quest 12 methods textbook - so definitely part of vce methods, but the question asked to sketch the graph on y = 9x-x^3 and its inverse using the CAS
You can easily sketch it without finding the actual equation of the inverse. Just reflect it along the line \(y=x\).

snowisawesome

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Re: VCE Methods Question Thread!
« Reply #15799 on: December 29, 2017, 07:47:44 pm »
0
You can easily sketch it without finding the actual equation of the inverse. Just reflect it along the line \(y=x\).
There was a question which asked to find the points of intersection between y = 9x-x^3 and it's inverse, in which case, you would need to know the equation of the inverse?

Also thanks everyone for the help so far

Eric11267

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Re: VCE Methods Question Thread!
« Reply #15800 on: December 29, 2017, 07:49:53 pm »
+2
There was a question which asked to find the points of intersection between y = 9x-x^3 and it's inverse, in which case, you would need to know the equation of the inverse?

Also thanks everyone for the help so far
To find the intersections between a graph and its inverse, you only need to find the intersections between the graph and the line y=x. Since the inverse is just a reflection in the line y=x, any points of intersection between a graph and its inverse will occur on the line y=x

RuiAce

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Re: VCE Methods Question Thread!
« Reply #15801 on: December 29, 2017, 07:54:10 pm »
+2
There was a question which asked to find the points of intersection between y = 9x-x^3 and it's inverse, in which case, you would need to know the equation of the inverse?

Also thanks everyone for the help so far

« Last Edit: December 29, 2017, 07:56:31 pm by RuiAce »

snowisawesome

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Re: VCE Methods Question Thread!
« Reply #15802 on: December 29, 2017, 07:56:18 pm »
0
To find the intersections between a graph and its inverse, you only need to find the intersections between the graph and the line y=x. Since the inverse is just a reflection in the line y=x, any points of intersection between a graph and its inverse will occur on the line y=x
Thank you :)

TheAspiringDoc

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Re: VCE Methods Question Thread!
« Reply #15803 on: December 30, 2017, 12:43:53 pm »
0
WHy is it said that natural numbers are 'a subset of or equal to' integers, not just 'a subset of' when using the sideways u symbol in set notation?

RuiAce

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Re: VCE Methods Question Thread!
« Reply #15804 on: December 30, 2017, 12:45:31 pm »
+1
WHy is it said that natural numbers are 'a subset of or equal to' integers, not just 'a subset of' when using the sideways u symbol in set notation?
Well, technically both are valid if you think about it

TheAspiringDoc

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Re: VCE Methods Question Thread!
« Reply #15805 on: January 01, 2018, 04:22:25 pm »
0
^^thanks Rui

For addition of ordinates questions, is it ok to sketch the two initial functions on the axes in addition to the resulting sum graph?
Also will we ever be asked to add 3+ graphs together?

VanillaRice

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Re: VCE Methods Question Thread!
« Reply #15806 on: January 01, 2018, 04:27:47 pm »
+3
For addition of ordinates questions, is it ok to sketch the two initial functions on the axes in addition to the resulting sum graph?
Also will we ever be asked to add 3+ graphs together?

I would personally recommend that you sketch the two initial functions first. It allows you to easily see all the significant points, such as intersections and x-intercepts. If you want to leave all 3 functions on the same axes, be sure to label each function (what I used to do is use dotted lines to draw the initial functions, and then draw the final function as a solid line). Otherwise, you can always carefully erase the two initial functions afterwards :)

Addition of ordinates questions have been relatively uncommon on VCAA exams in the past (they have been known to appear on SACs though), so I would say that it is unlikely that a question asking you to sketch the sum of 3 or more functions, but even if such a question is asked, the best method would be to do them one by one (i.e. adding two functions at a time).
« Last Edit: January 01, 2018, 04:29:36 pm by VanillaRice »
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snowisawesome

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Re: VCE Methods Question Thread!
« Reply #15807 on: January 02, 2018, 08:28:38 am »
+1
Are the multiple choice questions at the end of the chapter in Cambridge senior maths methods 3/4 textbook tech free or tech-active?

VanillaRice

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Re: VCE Methods Question Thread!
« Reply #15808 on: January 02, 2018, 08:48:05 am »
+2
Are the multiple choice questions at the end of the chapter in Cambridge senior maths methods 3/4 textbook tech free or tech-active?
Unless otherwise specified, MCQs are always tech active :)
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snowisawesome

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Re: VCE Methods Question Thread!
« Reply #15809 on: January 02, 2018, 09:12:28 am »
0
Unless otherwise specified, MCQs are always tech active :)
Thank you ;D