VCE Methods Question Thread!

[snowisawesome]

Yep to both questions

but if (2^x)^2 is the same as (2^2)^x
then (2^x)^2 would = (4^(x^2))
but (2^2)^x = (4)^x
Is there something i'm missing?

[VanillaRice]

but if (2^x)^2 is the same as (2^2)^x
then (2^x)^2 would = (4^(x^2))
but (2^2)^x = (4)^x
Is there something i'm missing?

Remember BIDMAS. The brackets on (4^(x^2)) imply the x is squared.

[snowisawesome]

Enclosed in spoiler because a reply was posted 36 seconds prior.

(Or a smaller subset of that interval.) The idea is that if \( x\notin (2,\infty) \), then \( g(x) \) is not defined. In a similar way, if \( f(x)\notin (2,\infty)\), then \(g\left[f^{-1}(x)\right] \) is not defined. The easiest way to make sure \(f^{-1}(x)\in (2,\infty) \) is true is to simply make the range of \(f^{-1}\) exactly that.

Regarding the edit:

Where did you get the f^(-1)(x) from?


What's the best way to utilise a group tutor in terms of asking questions (as it's harder to ask individual questions as it's not a private tutor)?

MOD EDIT: Merged double post//Sine

[Lear]

If someone could help me understand B I would be very grateful.
(Image attached)
Solution manual didn't make sense to me :/

[zhen]

If someone could help me understand B I would be very grateful.
(Image attached)
Solution manual didn't make sense to me :/

[Lear]

Damn I didn't see that.
Thank you so much Zhen

[Jigsaw]

Hey,

was wondering if anyone could show me how to do the following question:

state the dilation which maps the graph of f(x) to f1(x):

f(x)= 1/x^2, f1(x) = 5/x^2

I have the worked solution, but the problem is that its filled with too much jargon that is proving difficult to understand.  Thanks

[Yertle the Turtle]

Hey,

was wondering if anyone could show me how to do the following question:

state the dilation which maps the graph of f(x) to f1(x):

f(x)= 1/x^2, f1(x) = 5/x^2

I have the worked solution, but the problem is that its filled with too much jargon that is proving difficult to understand.  Thanks

For any given x value, what is the change in y values between f(x) and f1(x)?
For x=1, f(1)=1 and f1(x)=5
For x=2, f(2)=1/4 and f1(x)=5/4
For x=3, f(3)=1/9 and f1(x)=5/9

Therefore the dilation factor is 5

[Jigsaw]

For any given x value, what is the change in y values between f(x) and f1(x)?
For x=1, f(1)=1 and f1(x)=5
For x=2, f(2)=1/4 and f1(x)=5/4
For x=3, f(3)=1/9 and f1(x)=5/9

Therefore the dilation factor is 5

How would I then know if this is a factor of 5 from the x or y axis? Cheers

Edit: Its from the x axis because the y values are changing?

[GMT. -_-]

How would I then know if this is a factor of 5 from the x or y axis? Cheers

If it is a dilation of 5 from the x axis, then you change y to y/5 then rearrange for y, if it's a dilation from the y axis, you change x to x/5. Correct me if I'm wrong

[Yertle the Turtle]

I just checked it up, and a dilation from the x-axis is when (x,y) maps to (x,b*y) and a dilation from the y-axis is where (x,y) maps to (a*x,y). Hope this helps!

[Lear]

Honestly the above two ways confuse me. The way I simply remember it is a dilation from x axis means you multiply the entire function by a number.

E.g f(x)=1/x
Dilation from x axis by factor of 5
—> 5f(x) = 5/x

Since we are multiplying whatever comes out of f(x) by five, it means we are changing the y value as f(x) gives a y value.

This might be unorthodox and probably won’t make sense to many others but it helps me so it might help you

[Jigsaw]

This made more sense to me! So basically, the first step is to check if the whole function has been multiplied by something, or if only x has? This will tell us if a y value or x value is changing, and thus, if it is a or 1/a?

[Lear]

This made more sense to me! So basically, the first step is to check if the whole function has been multiplied by something, or if only x has? This will tell us if a y value or x value is changing, and thus, if it is a or 1/a?

Yup, it works for me

[jazzycab]

Honestly the above two ways confuse me. The way I simply remember it is a dilation from x axis means you multiply the entire function by a number.

E.g f(x)=1/x
Dilation from x axis by factor of 5
—> 5f(x) = 5/x

Since we are multiplying whatever comes out of f(x) by five, it means we are changing the y value as f(x) gives a y value.

This might be unorthodox and probably won’t make sense to many others but it helps me so it might help you

You need to be careful applying this for power functions, as dilations can be described correctly in either direction. For example the transformation for:

can be described as a:

This is because:

This might not seem important, as you can describe transformations however you like (provided they're correct), but consider a multiple choice question where only one option of the two is given, and you only know how to do it one way.