VCE Methods Question Thread!

[Splash-Tackle-Flail]

... Do you mean to post this on the Further thread, or is your textbook doing something weird?

No this is for methods- i did further last year! Ill upload a pic- it says to draw a line of best fit to find the dilation factor and y-int

Edit: This is from Mathquest if that helps!

[keltingmeith]

No this is for methods- i did further last year! Ill upload a pic- it says to draw a line of best fit to find the dilation factor and y-int

In which case, I can very safely say this isn't done in methods. You may be given n points, told the type of relationship, and then have to find the rule of the function - but you won't be given a bunch of coordinates and have to find the relationship connecting them. That is so much better done by regression techniques it isn't funny, and regression is definitely not covered in methods.

[knightrider]

This method can be applied to any polynomial - personally, I find that often it's hard to see this method, whereas division is a lot more concrete, but if you want to try it, go for it.

Thanks eulerfan101  yea i usually use division but for this particular polynomial this idea just popped in my head.
Also for division do you recommend short division or long division?Which ones quicker and convenient .

I believe the method is called "factoring by grouping" if you wish to do a little bit more research and see if it will be a viable method for you to use in the future.

Thanks Phy124 

[keltingmeith]

Thanks eulerfan101  yea i usually use division but for this particular polynomial this idea just popped in my head.
Also for division do you recommend short division or long division?Which ones quicker and convenient .

... I'm not quite sure what you're talking about when you say short or long division, but I'm assuming you do.

Regardless, my answer to this is my answer to every question about "which method is better?":

The one you can do fastest and with the least amount of mistakes is the better method. If one is faster, but the other is accurate, just work to make the other faster/accurate.

[knightrider]

... I'm not quite sure what you're talking about when you say short or long division, but I'm assuming you do.

Regardless, my answer to this is my answer to every question about "which method is better?":

The one you can do fastest and with the least amount of mistakes is the better method. If one is faster, but the other is accurate, just work to make the other faster/accurate.

True  Thankyou
What do you reckon will best set us up for methods 3/4 in terms of preparation?

[Zues]

that makes sense now since if i continued the graph past (3,1) it would pass through each respective x intercepts.

with these
c) how did they get x - 1 + 1, where did the -1 come from
d2)  2nd to third line, where did the e^loge go?

? 

[keltingmeith]

For , you should be aware that , as is the inverse of . In the first question you have and for the second, .

Pretty sure Conic answered you~

[Zues]

For , you should be aware that , as is the inverse of . In the first question you have and for the second, .

oh sorry missed this.

im not exactly sure what you mean, but i do know In(x) is the inverse of e^x.

[Conic]

If the point (x,y) lies on the graph of a one-to-one function f, then the point (y,x) will lie on the inverse, as the point gets reflected along the line y=x. So we know that and . Now (assuming the compositions are defined properly), we have



So when you compose a function with its inverse, the functions basically "cancel out" each other. If you plug x into the composition, you get x back, assuming x is in the appropriate domain. So and for each a>0 and for each real b because is the inverse of .

Note that the correct notation is ln(x) rather than In(x) (lower case L, not upper case i).

[Zues]

Yeap got it, thanks!

Also
1st screenshot) if the largest domain for a one to one function on the left hand side is (-inf,4) or (4, inf) on the right had side solution why cannot it be (-inf,1] or [1, inf) ?

2nd screenshot) for part a, f^-1(X) can exist for any set S, do they mean specifically for it to be a inverse function, i.e. then a one to one restriction for S?

[Conic]

Regarding the first screen shot, I would agree that the function would also have an inverse with the domain restricted to (-∞,1]. Regarding the second screen shot, they want S to be the restriction of the implied domain of the function so that it's inverse is also a function. In this case S = [1,∞), as the function is one-to-one over its implied domain, and hence its inverse is a function.

Somewhat off topic

The phrase "largest domain" is used a lot in methods. The intervals [1,∞) and [2,∞) contain the same number of elements, but in methods [2,∞) is considered "smaller".

From wiki: "Between any two real numbers a<b, no matter how close they are to each other, there are always infinitely many other real numbers, and Cantor showed that they are as many as those contained in the whole set of real numbers. In other words, the open interval (a,b) is equinumerous with ."

Cardinality of the Continuum

[strawberries]

for the range of a general parabola graph, the yintercept is (0,0) so it passes through 0, so from observations does the attached image mean the range is all Real positive numbers, including/or zero? Thanks

Yes, the U{0} just means that 0 is included.
If it was just R+ or R-, 0 wouldn't be included

Also, if     find

The book doesnt explain it. Can someone explain this in words, do we do the second one by wherever you see (x) you substitute in (x-1), if so why? Thanks

Yes, you do. It's just like if they asked you to find f(2), you'd substitute x with 2 in the equation.
so f(x-1) = 2(x-1)^2+(x-1) and you can expand that

[knightrider]

If a question says consider the points   and
 
and asks me to find AB

Does this mean the distance from A to B in which case i would use the distance formula.

or does this mean to find the line AB?

[keltingmeith]

If a question says consider the points   and
 
and asks me to find AB

Does this mean the distance from A to B in which case i would use the distance formula.

or does this mean to find the line AB?

This is just a poorly written question. In ANY VCAA exam, they will be more obvious as to if they want the line or the distance. In a SAC, just ask your teacher - if they don't want questions, they'll write the SAC better.

[knightrider]

How come when writing notation in maths.

Whenever infinity is mentioned it is always in closed brackets. eg

why cant it be in square brackets eg

Is there a reason behind this?