VCE Methods Question Thread!

[kinslayer]

Why is the co domain R and is it always R?

As Thorium said, you can think of the codomain as the type of object the function spits out. In higher mathematics this is not always a number, but in Methods it is always a (real) number and this is why the codomain will usually be given as R. If a function only gives whole number outputs then the codomain might instead be Z (integers) or N (natural numbers/positive integers).

The range of a function is always a subset of its codomain.

[Jason12]

[kinslayer]

(Image removed from quote.)

The derivative is

This is equal to zero when

Taking logs of both sides we can see that this is only true when x = 0, at which point f(x) = 2. We can confirm that this is a minimum by checking f'(-1) and f'(1).

[knightrider]

What would be the dilation factor for the following graphs
y=1/2(x-4)^2 =3
y=-2/3(x-4)^2 +2
y=-1/3x-6

What transformations do the following graphs have
y=abs value 3(x+3)^2 -2
y=abs value  -3(x+3)^2 -2
y=-abs value  3(x+3)^2 -2
y=-abs value  -3(x+3)^2 -2

[paper-back]

What would be the dilation factor for the following graphs
y=1/2(x-4)^2 =3
y=-2/3(x-4)^2 +2
y=-1/3x-6

Dilated by factor of 1/2 from the x axis
Dilated by factor of 2/3 from the x axis
Dilated by factor of 1/3 from the x axis

[soNasty]

a conical flask with a radius of 5cm and a height of 12cm is being filled so that its height is changing at a rate of cm/min. Find the rate at which the volume is changing.

[Cort]

Quick question: When the question asks you to find the 'minimum' value - that's basically asking you to find the point where it would be a minimum gradient, correct? Since it is after all dy/dx=0? If that's the case, then how would we know if that dy/dx=0, since the nature of the stationary points can be either a point of inflection, min or max? I understand how to do it, but not why.

[Thorium]

Quick question: When the question asks you to find the 'minimum' value - that's basically asking you to find the point where it would be a minimum gradient, correct? Since it is after all dy/dx=0? If that's the case, then how would we know if that dy/dx=0, since the nature of the stationary points can be either a point of inflection, min or max? I understand how to do it, but not why.

Since we know that there is three different types of SPs and we are looking for the local min. one, then we have find the Nature and see if it is local min. One way to do this is to substitute into the gradient function an x value more than and less than the x value at dy/dx=0. This way we get an idea of how the graph looks like. For our case, if the resultant gradients are negative-zero-positive (\ _ /), then we will know that this is a local minimum

[Thorium]

a conical flask with a radius of 5cm and a height of 12cm is being filled so that its height is changing at a rate of cm/min. Find the rate at which the volume is changing.

Is the answer in terms of height or is it just a number?

[soNasty]

[Thorium]

I have attached the solutions

[soNasty]

ohh so its like a cone. alright thanks man

[paper-back]

A cuboid with a square base is to be made from 200cm2 of material
Show that the height, h=50/x-x/2, where x is the side length of the base

How do you get width? In the solutions manual it states that width is x
Thanks

[Einstein]

for the truncus, it says in my notes that the range: y>c (if a>0) or y<c (if a<0) whats this mean?

thanks

edit: i know what the term 'range' is, but im just wondering what the above means, if you could also give an example that would be gold.

[paper-back]

for the truncus, it says in my notes that the range: y>c (if a>0) or y<c (if a<0) whats this mean?

thanks

edit: i know what the term 'range' is, but im just wondering what the above means, if you could also give an example that would be gold.

I think it means this:
C is the verticle translation, and hence if a>0 meaning a is positive, (hence no reflection in the x axis), y(the function)>c(the verticle translation)
Howevever,
If a<0, (there is a reflection in the x axis) then y(the function)<c(the verticle translation)

An example:
Draw the graph of y=3/x^2 + 2 and the graph of -3/x^2 + 2 on the same axis
You'd see that the latter one  is reflected in the axis and hence the function is less than 2(the verticle translation or c)

Just what I think it means, not sure if correct