My Methods 3/4 questions thread

[smile+energy]

Transformations involved
1. Reflection over the x-axis
2. Dilation by a factor of 1/4 from y-axis
3. Horizontal translation of 1 unit in the negative direction
4. Vertical translation of 3 units upwards


Matrix equation

1/4  0     X    +  -1
0    -1    Y         3



There are meant to be brackets around the matrices but the formatting goes off..

That's awesome, thanks so much

[smile+energy]

Can I please get some help? the changes necessary to the graph of y=x^3. a) y=4(2-x)^3; b) y=-6(7-x)^3, I am confused for the reflection in the equations.
Thanks

[smile+energy]

Taking the three from the bracket initially?
So y'-1=27(x'-2)^3 => (y'-1)/27 = (x'-2)^3

There is now no dilation from the y axis and the dilation now occurs from the x axis factor 1/27.

Hi Lzxnl, may I ask where is the 27 come from?

[lzxnl]

(3x-6)^3 = (3(x-2))^3 = 3^3*(x-2)^3 = 27(x-2)^3

[smile+energy]

(3x-6)^3 = (3(x-2))^3 = 3^3*(x-2)^3 = 27(x-2)^3

Thanks

[Angur.Angel]

Can someone please factorise x^2+14x+6-x^3

[drake]

let p(x) = -x^3 + x^2 + 14x + 6

so p(-3) = -(-27) + 9 - 42 +6 = 0 => (x+3) is a factor of p(x)

now you just do long division to find the quadratic.. and then see if you can factorise the quadratic. i assume you know how to do this.

[smile+energy]

Can I get some help?
If I work out the inverse function of y=5ln(3x-2), do I must write the domain of inverse function? Do I need to write the domain of inverse functions in other questions as well? I am really confused.
Thanks in advance.

[Zealous]

Can I get some help?
If I work out the inverse function of y=5ln(3x-2), do I must write the domain of inverse function? Do I need to write the domain of inverse functions in other questions as well? I am really confused.
Thanks in advance.

If a question asks for the inverse function, you must specify the domain as part of function notation.
eg: (see VCAA 2009 Methods Exam 1 Q3)

If a question asks for the rule of an inverse function, you do not need to show the domain.
eg: (see VCAA 2006 Methods Exam 1 Q2a)

[GeniDoi]

Are non-constant asymptotes (eg y = x or y = x^2) part of the Methods design?

[smile+energy]

If a question asks for the inverse function, you must specify the domain as part of function notation.
eg: (see VCAA 2009 Methods Exam 1 Q3)

If a question asks for the rule of an inverse function, you do not need to show the domain.
eg: (see VCAA 2006 Methods Exam 1 Q2a)

That's clear. Thanks

I don't understand the part in your first example, which is before the f(x) function, can you tell me what does it mean? That will be great.

[Daenerys Targaryen]

It reads as: f such that from 0, inclusive, to infinity maps onto the Reals, for the fucntion f(x)=x^2

So the first bit is usually the name of the function, the [0,inf) is the domain. The R means what number system you're using. And then the last bit is just the function. i.e. y=x^2

[Daenerys Targaryen]

Are non-constant asymptotes (eg y = x or y = x^2) part of the Methods design?

Yes, when doing addition of ordinates

[smile+energy]

It reads as: f such that from 0, inclusive, to infinity maps onto the Reals, for the fucntion f(x)=x^2

So the first bit is usually the name of the function, the [0,inf) is the domain. The R means what number system you're using. And then the last bit is just the function. i.e. y=x^2

Thank you

[smile+energy]

Hi, there

Can I get some help?
For solving an inverse function. In what type of question,  do I have to use matrix to deal with it?