VCE Methods Question Thread!

[Jenny_2108]

Quick question:

Write down the derivative of as a hybrid function.

The answer is:



Though I agree with it, why is it (and not )? Isn't it not differentiable at when due to the modulus?
(Note the question is also in MAV 2008 Exam 2)

f(x) is not differentiable at end point/sharp point/discontinous

[catwoman101]

y=6x^2+4kx=k=3

find the yint in terms of K

and find the discriminant ?

[soccerboi]

Shouldn't the constant 'c' also be divided by 3?

[Homer]

c1 divided by 3 equals c

[soccerboi]

c1 divided by 3 equals c

I'm confused. Why didn't they just write 'c1' as 'c' and then write it as (c/3) ?

[paulsterio]

I'm confused. Why didn't they just write 'c1' as 'c' and then write it as (c/3) ?

It doesn't matter, a constant divided by a constant is still a constant.

[soccerboi]

Oh ok Thank you.

I need help with adjusting the domain with the attached question, can't seem to get it right.
a is suppose to be equal to 1/18 and 11/18

[polar]

Clearly, is one period, so

[Homer]

solve for

pi/3 = 3pi( 1/6 -a) , a would equal 1/18
2pi/3 = 3pi( 1/6 -a) , a would equal 1/18
7pi/3 = 3pi( 1/6 -a) , a would equal 11/18

[soccerboi]

Ok thanks heaps guys

[HERculina]

You know when there's a dilation parallel the the x-axis/from y, the vertical asymptotes are affected yeah? So would you multiply it by the factor it's dilated by? And then if their are any translations in the x-axis you apply those afterwards?

[BubbleWrapMan]

Yes and yes

[Special At Specialist]

You know when there's a dilation parallel the the x-axis/from y, the vertical asymptotes are affected yeah? So would you multiply it by the factor it's dilated by? And then if their are any translations in the x-axis you apply those afterwards?

Yes, you do it in that order. For example:
y = tan(x) has asymptotes at x = pi/2, 3pi/2, 5pi/2, 7pi/2 ...
y = tan(3(x + pi/2)) has asymptotes at x = -pi/3, 0, pi/3, 2pi/3 ...
You divide by 3 first (eg. (3pi/2) / 3 = pi/2) and then you subtract pi/2 (pi/2 - pi/2 = 0)

[HERculina]

Oh I see, does this happen to the horizontal asymptotes if you have a dilation parallel to y-axis? This is probably a stupid q. but why doesn't y=-4e^(x/2)+1 have a asymptote of y=4 but just y=1?

[Special At Specialist]

Oh I see, does this happen to the horizontal asymptotes if you have a dilation parallel to y-axis? This is probably a stupid q. but why doesn't y=-4e^(x/2)+1 have a asymptote of y=4 but just y=1?

Because the dilation has to affect the entire equation. For example, if y = f(x) has an asymptote at y = 1, then y = 4*f(x) will have an asymptote at y = 4.
In this case, f(x) = -e^(x/2) + 1 and 4f(x) = -4e^(x/2) + 4
You are essentially calculating the asymptote of y = 4*f(x) - 3
So if the asymptote of y = f(x) is at y = 1, then for y = 4*f(x) - 3:
4*1 - 3 = 1
So the asymptote stays the same.