VCE Methods Question Thread!

[cosine]

Also, what is the difference between R+ and R+ U {0}
What do they mean and how does it affect the domain?

[keltingmeith]

Also, what is the difference between R+ and R+ U {0}
What do they mean and how does it affect the domain?

is only positive real numbers - 0 is neither positive or negative, so it's not in the first one.

[IndefatigableLover]

OH so you are saying that although y=6 is the first y value, it doesnt matter, so to find out the range we have to consider the LOWEST y value to the HIGHEST?

Yes that's right It becomes a lot easier (these types of questions) as time goes by but do be aware since people do gloss over this without giving it a second thought (not for quadratic equations but more so for trigonometric equations) so always remember to plot the graph!

Also, what is the difference between R+ and R+ U {0}
What do they mean and how does it affect the domain?

The first one is all positive real values whilst the other one is all positive real values including zero (for your domain). Since zero isn't positive, it isn't included when someone writes R+. To include zero, you would need to write it in the latter form.

[cosine]

is only positive real numbers - 0 is neither positive or negative, so it's not in the first one.

Awesome, thanks!
We were just assumed to know these signs in class without being taught... I managed to teach myself all the other symbols and their meaning but couldnt decide whether 0 was a positive number or a negative lol

[cosine]

Yes that's right It becomes a lot easier (these types of questions) as time goes by but do be aware since people do gloss over this without giving it a second thought (not for quadratic equations but more so for trigonometric equations) so always remember to plot the graph!
The first one is all positive real values whilst the other one is all positive real values including zero (for your domain). Since zero isn't positive, it isn't included when someone writes R+. To include zero, you would need to write it in the latter form.

Totally get it now, thanks so much!!

[lzxnl]

OH so you are saying that although y=6 is the first y value, it doesnt matter, so to find out the range we have to consider the LOWEST y value to the HIGHEST?

I went to the supermarket on ten days, and bought, respectively, 10, 9, 8, 7, 6, 5, 5, 3, 1, 1 bags of chocolate on each day. Now, if you define a function f(t) where t is the time in days and f is the number of bags of chocolate bought on day t, the range of f is {1,3,5,6,7,8,9,10}
See how the order has changed? The 'range' is always ordered from lowest to highest.

[cosine]

I went to the supermarket on ten days, and bought, respectively, 10, 9, 8, 7, 6, 5, 5, 3, 1, 1 bags of chocolate on each day. Now, if you define a function f(t) where t is the time in days and f is the number of bags of chocolate bought on day t, the range of f is {1,3,5,6,7,8,9,10}
See how the order has changed? The 'range' is always ordered from lowest to highest.

Yeah it makes sense now, thanks a lot, its just that sometimes the symbols and mathematical jargon just gets to me, but im getting there!

And seeing that you obtained outstanding results in VCE, may I ask you a question about preparation in the summer holidays before commencing year 12?

[lzxnl]

Yeah it makes sense now, thanks a lot, its just that sometimes the symbols and mathematical jargon just gets to me, but im getting there!

And seeing that you obtained outstanding results in VCE, may I ask you a question about preparation in the summer holidays before commencing year 12?

In that set of summer holidays? I read through the chemistry textbook, did an English Language assignment...and that was sort of it
Most of the work I did for VCE was either for English Language in year 12 or before year 12. I did all my VCE maths subjects before end of year 10 so yeah. Lots more time in years 11 and 12 for other things.

[cosine]

In that set of summer holidays? I read through the chemistry textbook, did an English Language assignment...and that was sort of it
Most of the work I did for VCE was either for English Language in year 12 or before year 12. I did all my VCE maths subjects before end of year 10 so yeah. Lots more time in years 11 and 12 for other things.

Thanks haha, and well done on your results!!

[Zues]

if something i dilated by 1/2, why cant we just do y=1/2(x-3)^4 for example and why is it y=(2x-3)^4 ??

also what is the difference between y=-1/2 x^3 - 3 and y= (-2x^3)^3 - 3

and also y= - (2x-4)^4    and  y=(4-2x)^4

[Zues]

how did they take the 4 out?

[DSubShell]

how did they take the 4 out?

I didn't know which step was confusing you, so I wrote it all out

[cosine]

if something i dilated by 1/2, why cant we just do y=1/2(x-3)^4 for example and why is it y=(2x-3)^4 ??

also what is the difference between y=-1/2 x^3 - 3 and y= (-2x^3)^3 - 3

and also y= - (2x-4)^4    and  y=(4-2x)^4

This is because anything inside the brackets and is the coefficient of 'x', it is a dilation in the x-axis, so if you are stating the dilation which is inside the brackets, for example (3x-3)^2, it would be 1/a and 'a' as in the coefficient of 'x'. So it is dilated by a factor of 1/3 parallel to the x-axis.

[Zues]

ok i see how that happens, but why is it that? is there proof?

because (3x-3)^2 can because 3(x-1)^2 is the dilation 3 now? do i get the dilation in its expanded form or factorised form e.g. a(x-b)^n +c where a is dilation,??

[cosine]

ok i see how that happens, but why is it that? is there proof?

because (3x-3)^2 can because 3(x-1)^2 is the dilation 3 now? do i get the dilation in its expanded form or factorised form e.g. a(x-b)^n +c where a is dilation,??

Bro, there can be two separate dilations on a function, the dilation outside the brackets will only affect the y-values, meaning that the x-values will remain the same but the y-values will be 'DILATED' by a factor of whatever the factor is.

Take for example 2(x-1)^2

- There is a dilation of 2 PARALLEL TO THE Y-AXIS, why though?
 Well, say our first value of 'x' is 1 and to compare and make it easy for you to understand I will do both with and without the dilation factor so you can understand.

Note that I am working out for the y-values as we are substituting in the x-values:
(1-1)^2 = 0
(2-1)^2 = 1
(3-1)^2 = 4

Now try with the dilation factor:
2(1-1)^2 = 0
2(2-1)^2 = 2
2(3-1)^2 = 8

Now, my x-values (1, 2 and 3) did not change, but my y-values did change, they doubled. Well if you visually see this, it means that the x-values are remaining the same and the y-values are getting larger and larger, so the graph is approaching the y-axis rapidly (hence why dilation parallel to y-axis, meaning it is dilating or closing into the y-axis). Draw this on your CAS and it will make you understand it better!

I dont know why the dilation is 1/a when you are dealing with a coefficient of 'x', but I do know why its parallel to the x-axis and not y-axis.
For example:

f(x) = 2(x-1)^2 can also be written f2(x) meaning that the whole function is multiplied by a factor of 2 which will result in a dilation parallel to the y-axis (as demonstrated above)

So what does f(2x) mean? This means there is a dilation by factor of 1/2 (i dont know why its 1/2 instead of 2), but this means the whole function isn't multiplied by 2, but only the 'x' values as the 2 is infront of the x. So, if the x-values are getting larger and the y-values remain the same, the graph will be dilated parallel to the x-axis (in other words it is expanding or approaching the x-axis rapidly).

I hope this helps mate, Im also doing year 12 next year so Im no expert at this stuff, but I hope you took something from it!