VCE Methods Question Thread!

[One Step at a Time]

Hi everyone,

I thought I understood the concept of one-to-one functions e.g. horizontal line test in Units 1/2, but I can't get my head around the Essential Maths Textbook's explanation.

I've attached a pic of what's written in the textbook.

Would greatly appreciate if someone could tell me what they're talking about! Thanks 

[Buddster]

Hi everyone,

I thought I understood the concept of one-to-one functions e.g. horizontal line test in Units 1/2, but I can't get my head around the Essential Maths Textbook's explanation.

I've attached a pic of what's written in the textbook.

Would greatly appreciate if someone could tell me what they're talking about! Thanks 

They're pretty much describing the line test but with more mathematical language.

Let's say f(x)=x²
and a=-3 and b=3

f(a)=9 AND f(b)=9, therefore the functional fails the line test (and a and b are different). For the line test to work, there can't be 2 different numbers for x that have the same y value

Does this help?

[Sine]

Hi everyone,

I thought I understood the concept of one-to-one functions e.g. horizontal line test in Units 1/2, but I can't get my head around the Essential Maths Textbook's explanation.

I've attached a pic of what's written in the textbook.

Would greatly appreciate if someone could tell me what they're talking about! Thanks 

The textbook has quite an unecessary explanation imo. The simplest explanation is for each unique x value there is only a single unique y-value and the easiest way as you say is to do the horizontal line test and the vertical line test.

The textbook is saying that the only way 2 particular x -values produces the same y - value is when the x-value are the same hence only a single x-value for each y-value.

[One Step at a Time]

Ah finally got it after a good few minutes lol, thanks so much

Still unsure about f(a)=f(b) though. How does this indicate that a function is one-to-one? 

They're pretty much describing the line test but with more mathematical language.

Let's say f(x)=x²
and a=-3 and b=3

f(a)=9 AND f(b)=9, therefore the functional fails the line test (and a and b are different). For the line test to work, there can't be 2 different numbers for x that have the same y value

Does this help?

[Sine]

Ah finally got it after a good few minutes lol, thanks so much

Still unsure about f(a)=f(b) though. How does this indicate that a function is one-to-one? 

So when you solve f(a)=f(b) you arrive at the result a=b this indicates that only when a=b so does f(a)=f(b) i.e a,b=3 this follows that f(3)=f(3) and 3=3 . Consider if we arrive at a result such that a=/=b this would indicate that two different x -values (a and b) arrives at the same y-value hence an indication that it is not one to one hence when a=b this indicates it is one to one.

[One Step at a Time]

Thanks so much Sine  Understand all that maths language now haha 

[One Step at a Time]

Hi everyone,

For 14a) (in the attached pic), why don't we sub x=4 into only f(X)=2x, and not f(x)=1/x?

Thanks 

[MightyBeh]

Hi everyone,

For 14a) (in the attached pic), why don't we sub x=4 into only f(X)=2x, and not f(x)=1/x?

Thanks 

because -4 is less than 3, we use f(x)=2x because the other is undefined for x=-4. 

[One Step at a Time]

because -4 is less than 3, we use f(x)=2x because the other is undefined for x=-4. 

Haha I sat there for a solid minute wondering, but everything's so clear now haha

Thank you so much 

[Gogo14]

1. I don't know why I didnt get full marks for 4.b.
http://imgur.com/OXp7epD
2. Is probability involving permutations, combinations on the 3/4 course?Dont think it was on study design, but Im really bad at them. Is it worth revising?

[Buddster]

1. I don't know why I didnt get full marks for 4.b.
http://imgur.com/OXp7epD
2. Is probability involving permutations, combinations on the 3/4 course?Dont think it was on study design, but Im really bad at them. Is it worth revising?

1. The line through the x makes me thing the teacher read it as a "x" not a multiplication symbol. Clearer working may have been needed to split up the parabola and rectangular area. Alternatively, the question requests you use calculus, so you may have had to define the line SR as y=3 and then integrate it.
2. They are indeed, but in a different manner (especially combinations). Would be a good idea to revisit.

[keltingmeith]

Buddster gave some good answers, but thought I'd add on:

1. I don't know why I didnt get full marks for 4.b.
http://imgur.com/OXp7epD

You should PROBABLY ask your teacher, then. We didn't mark it, all we can do is make guesses (as Buddster did) - meanwhile, your teacher can give ACTUAL feedback on this stuff.

2. Is probability involving permutations, combinations on the 3/4 course?Dont think it was on study design, but Im really bad at them. Is it worth revising?

You only need to know how to calculate nCr. It's nice if you can understand the concepts, and it helps a lot in probability (as Buddster mentioned - particularly for the binomial distribution) but they're REALLY unlikely to ask you any questions specifically regarding this stuff.

[Drewballs]

Does anyone know of a good summary of all the graphs we use in methods to use as a poster for my desk?

[Buddster]

Does anyone know of a good summary of all the graphs we use in methods to use as a poster for my desk?

[geminii]

(Image removed from quote.)

Wow this is amazing!!