VCE Methods Question Thread!

[Jenny_2108]

Yeah I understood that part
But don't you need to do anything after that? To give the answer in terms of ?

Giving ans in term of in this ques just mean you let one variable (x or y depending on you) = because you already know z=5 then express the other variable in term of from the equation given

( my explanation is so lollll )

[~T]

Just a query, when writing sums of functions, products of functions, or composite functions, what are the accepted ways of writing them?

For example, can you use function notation such as:

?

Thank you

[brightsky]

that's fine. i always just wrote f(g(x)), but yeah whatever floats your boat. just be wary of the domain.

[FlorianK]

Just a query, when writing sums of functions, products of functions, or composite functions, what are the accepted ways of writing them?

For example, can you use function notation such as:

?

Thank you

I'm not sure, but it definetly isnt , because it is not defined for, for example x=-1

[#1procrastinator]

I never figured out this question:

Consider the function
i) Show that f(x) has stationary points at minus root 2 and plus root 2
ii) Find values of a for which y=f(x) crosses the x-axis at 3 distinct points

I can do i) but not sure how to do ii)

EDIT: the function is ax^3-6ax+12 in case tex isn't working

[Homer]

shouldn't it be -6ax?

[#1procrastinator]

When you find the stationary points for this function, it turns out there are none. That is, no real solutions ( ). Is that the function the question really states?

shouldn't it be -6ax?

Yep, sorry, fixed

[Phy124]

I never figured out this question:

Consider the function
i) Show that f(x) has stationary points at minus root 2 and plus root 2
ii) Find values of a for which y=f(x) crosses the x-axis at 3 distinct points

I can do i) but not sure how to do ii)

EDIT: the function is ax^3-6ax+12 in case tex isn't working

i) Stationary points occur when the derivative is zero:









ii) It will cross at three distinct points when one of the stationary points is above the x axis and the other below (Two will occur when one is above or below and the other lies on the x axis, one will occur when both are above or below the x-axis.

We are given the condition that therefore we have a positive cubic and the left most stationary point will be above the right most stationary point.

This means to fit our condition of three unique roots, the right most stationary point needs to be below the x-axis.

The right most stationary point always occurs at , which has the y value:



We want this y value to be less than zero, so:

[Will T]

Chapter 1 chapter review extended response question 7b (essentials)

State why gof is a function.
The answer says that 'gof is one-to-one' and therefore a function.
I'm pretty sure relations can be one-to-one, for example the graph of + and - root x.
So their logic seems somewhat invalid.
How would you answer this though, I said "every pre-image projects a unique image, therefore it is a function" and I know quoting the definition of a function using jargon doesn't really justify, but I mean it's obviously a function though.

[TrueTears]

Chapter 1 chapter review extended response question 7b (essentials)

State why gof is a function.
The answer says that 'gof is one-to-one' and therefore a function.
I'm pretty sure relations can be one-to-one, for example the graph of + and - root x.
So their logic seems somewhat invalid.
How would you answer this though, I said "every image has a unique pre-image, therefore it is a function" and I know quoting the definition of a function using jargon doesn't really justify, but I mean it's obviously a function though.

define

Let X be the set , define Y to be such that

we now show that , exactly one such that

Assume we take , such that and where which clearly leads to a  contradiction, so h is a function.

[BubbleWrapMan]

It should be "every pre-image has a unique image" if I'm remembering right

[Will T]

Ahh yes it is, that was a fail.

[zvezda]

A car travels half the distance of a journey at an average speed of 80km/h and half at an average speed of x km/h.
Define a function, S, which gives the average speed for the total journey as a function of x.
Help is appreciated

[b^3]

Look back a couple of pages in this thread and you'll find it.

Let be the total distance of the journey.



EDIT: Fixed the minor screw up

EDIT: Ok latex is broken.....

Give me a min to fix...

s=d/t
t=d/s
t_{1}=(d/2)/80
         =d/160
t_{2}=(d/2)/x
         =d/2x
t_{total}=t_{1}+t_{2}
               =d/160+d/2x
               =dx/160x+80d/160x
               =d(x+80)/160x
S_{avg}=d_{total}/t_{total}
              =d/(d(x+80)/160x))
              =d*160x/(d(x+80))
              =160x/(x+80)

Hope that readable...

[zvezda]

Look back a couple of pages in this thread and you'll find it.

latex isnt working