VCE Methods Question Thread!

[cosine]

Answer is A. When you sub in everything it becomes
Sub in for the asymptote, and you get and tan(pi/2) is undefined hence an asymptote.
To find your first asymptote, you can always let everything inside the tan (in this case 4x) =pi/2 and solve for x.
so


I'm not sure why you need the next x-intercept though, cause the question is about asymptote and period

My teacher HEAVILY stresses it's D though :/  Why would this be so?

[cosine]

How would you write a general equation for a exponential function which is dilated from the y-axis and translated horizontally.

Where a and b are constants.

[knightrider]

Where a and b are constants.

How did you get the +b on the outside doesn't that mean vertical translation?

So would it be

[99.90 pls]

Find the point(s) on the arc of the parabola y = x^2 for [0, 1] which are nearest to the point (0, m).

[RKTR]

Which points(s) on the curve of y=x^2 is/are nearest to the point (0,2)?

How would you answer this thank you?

Distance = root of [(x-0)^2 + (y-2)^2]
D=root of [ x^2 + (x^2 -2)^2]
D= root of [ x^2 + x^4 -4x^2 +4]
D= root of [ x^4 -3x^2 +4]

dD/dx = [1/2 (4x^3 -6x)] / root of [x^4 -3x^2 +4]
shortest/longest distance when dD/dx=0
4x^3 - 6x =0
2x(2x^2-3)=0
x=0 or x= +- root(3/2)

x=0,D=2   x=+- root(3/2),D=root(7)/2

answer =(0,0)

[cosine]

Solve 2sin(3x-pi/4) = -1 over (-pi, pi]

Im having troubles with the domain change, thanks!

[qwerty101]

had bit of a blank.

for questions where they give you an equation with evident transformations already been applied, and they ask show the matrix that produces the one given from a base one (i.e. y=e^x). if the transformed one shows a dilation of 1/2 from the y axis i.e. e^2x, do we put it in matrix form as 1/2 or with a 2?

alternatively, if i have a question that says show the matrix a with a dilation factor of k from y axis, do i put k or 1/k ?

[wunderkind52]

Solve 2sin(3x-pi/4) = -1 over (-pi, pi]

Im having troubles with the domain change, thanks!

Assuming you mean solving for x
Since , naturally
Now, solving,



Then, rearranging -
and finally


With the domain, I always like to think of it as applying the same operations to the domain as you do to the variable.
Consider this scenario, we are playing a "guessing game". I have to pick a number, and you have to guess what that number is.
I have to pick a random number (which we will call A) that lies between 0 and 10. (Don't rant about sets and integers - this is purely for demonstrative purposes)
Ok, now, my directions are - first - to multiply the number by 2.
If you were to guess my number (final number) at this point, would you agree that you would guess any number between 0 and 20? If I chose the smallest number 0, and multiplied this by 2, I would still have 0. But if I chose 10 to start with, this would now become 20. So, therefore
Now, If you told me to subtract 3 from this number (already multiplied by 2). The possible numbers now be . If I started with 0, multiply it by 2 and subtract 3 - that's -3. If i start with 10, multiply it by 2 and subtract 3 - that's 17.

Going back to the question - If you know that x lies between -pi and pi, then 3x lies between -3pi and 3pi, and 3x-pi/4 lies between -3pi-pi/4 and 3pi-pi/4!
I hope this analogy of sorts wasn't too convoluted and pointless -I have a tendency to do that

My teacher HEAVILY stresses it's D though :/  Why would this be so?

Hahahha I can't really explain to you why an incorrect answer is correct. (I don't do debating)

[cosine]

Assuming you mean solving for x
Since , naturally

Can you pls elaborate on this step?

Thanks so much!!

[wunderkind52]

Can you pls elaborate on this step?

Thanks so much!!

See my previous post - I added it there!

[knightrider]

Where a and b are constants.

Cosine is this incorrect from above?

IHow did you get the +b on the outside doesn't that mean vertical translation?

So would it be

[cosine]

Cosine is this incorrect from above?

IHow did you get the +b on the outside doesn't that mean vertical translation?

So would it be

I misread, I tend to do that lately

It really depends on how the question is worded, if it says dilated, THEN translated then it would be:

[99.90 pls]

Find the point(s) on the arc of the parabola y = x^2 for [0, 1] which are nearest to the point (0, m).

Whoever can solve this question shall be crowned the king/queen of Camelot.

[cosine]

In regards to application questions, if they don't specify what decimal place to round off to, and we get something like 12.99 or 15.49 can we automatically round off or not? Thanks

[Redoxify]

f(x) = 1-sin pi(x+1), work out x intercepts