VCE Methods Question Thread!

[A TART]

Does it matter which questions I do from a particular exercise?
I'm currently attempting a few chapters of chapter 2 from mathsquest and following my school's suggested questions but if the suggested questions change next year, then will it make a difference weather i do the new set of suggested questions or the old set of suggested questions?

The study design and the textbook is still the same so I don't think it'll affect you. The only reason the school might change the questions is to cater for this year's class (depending if they overall are considered "strong" at maths). At least this is what happens at my school.

Edit: Fixed all the grammatical mistakes. Today is not my day.

[snowisawesome]

Can someone please explain the addition of ordinates rule? I've read it in my textbook but it still doesn't quite make sense yet

[zhen]

Can someone please explain the addition of ordinates rule? I've read it in my textbook but it still doesn't quite make sense yet

For addition of ordinates, you basically add the y-values together. Let’s say you have a function h(x)=f(x)+g(x)
f(x)=x and g(x)=x²
To find h(0) you add f(0)+g(0). So, you add the y-values together to get h(x). In this case h(0)=0²+0=0 This is basically addition of ordinates. If you want to find h(3), it’s just f(3)+g(3). h(3)=3+3²=12 You’re adding together the y-values corresponding to the same x-value. I think that was a bit confusing, so let me know if you want me to explain it further.

[Bri MT]

Can someone please explain the addition of ordinates rule? I've read it in my textbook but it still doesn't quite make sense yet

So in a function you have an input (x value) and you get an output (y value)
When you add functions together, you add the y-values of all of the functions you are adding to get your new y-value.
So for example if you had g(x)= x^2   and f(x)=2x+3  and were asked to graph f(x)+g(x)  you could pick some points
e.g.  when x=2, g(2)=4 and f(2)=7  thus g(2)+f(2)=11
when x=0, g(0)=0, f(0) = 3  thus g(0)+f(0)=3
you could do this for as many x values as you wanted to, but remember that f(x)+g(x) is ONLY defined when both f(x) AND g(x) are defined

A nice thing about this technique is that you can use it to draw the graph of f(x)+g(x), based on their individual graphs, without knowing what rule each graph follows as you only need to know the co-ordinates. Eg. At the intersection of two graphs, you know that the new y-value will be 2 times the original value, without having to know how the original values were made.

[snowisawesome]

MOD EDIT: remove request for copyrighted materials

[snowisawesome]

f(x) = x^2 + 1
g(x) = √(x)

would the range of g(x) be a subset of the domain of f(x)
?

[zhen]

f(x) = x^2 + 1
g(x) = √(x)

would the range of g(x) be a subset of the domain of f(x)
?

Range of g(x)=[0,infinity)
Domain of f(x)=R
Does the range of g(x) fall under the domain of f(x)? If it does, then it’s a subset.

[snowisawesome]

Range of g(x)=[0,infinity)
Domain of f(x)=R
Does the range of g(x) fall under the domain of f(x)? If it does, then it’s a subset.

I think the range of g(x) falls under the domain of f(x)? So it's a subset

[zhen]

I think the range of g(x) falls under the domain of f(x)? So it's a subset

Yup. Cause the domain of f(x) is basically all real values, whereas the range of g(x) is [0,infinity) which are values which are included in the domain of f(x).

[snowisawesome]

If f: (0, infinity) → R, f(x) = 1/x, g:R\{0} → R, g(x) = 1/x^2

would the range of f(x) be R or (0, inifinity), because the answer in my book says (0, infinity), but I think it's R

[Bri MT]

If f: (0, infinity) → R, f(x) = 1/x, g:R\{0} → R, g(x) = 1/x^2

would the range of f(x) be R or (0, inifinity), because the answer in my book says (0, infinity), but I think it's R

So in this there are two components  to really consider.
1. The x is squared -> can only produce values of [0,inf)
2. 1 is divided by the squared x ->  0 is not an allowable value      Thus the range is (0,inf)

[snowisawesome]

Do you need 100/100 sacs and 40/40 and 80/80 on exams to get a premier's award in methods? Since not everyone that gets a 50 gets a premiers award?
Also, thanks miniturtle for the help

If f(x)= x^2 and g(x) = √(x)

f(g(x)) = (√(x))^2 = x
I thought the domain of f(g(x)) would be R, but my book said that it would be [0, infinity)
Is this because the domain of g(x) = [0, infinity), and the composite function is f(g(x))
?

Mod edit: EDIT PREVIOUS POST

[Syndicate]

If f(x)= x^2 and g(x) = √(x)

f(g(x)) = (√(x))^2 = x
I thought the domain of f(g(x)) would be R, but my book said that it would be [0, infinity)
Is this because the domain of g(x) = [0, infinity), and the composite function is f(g(x))
?

Dom f(g(x)) = dom g(x) given that the range of g(x) is the subset of the domain of f(x). In this g(x) is sqrt(x), and its domain is [0, infinity), hence dom f(g(x)) is [0, infinity).

[zhen]

If f(x)= x^2 and g(x) = √(x)

f(g(x)) = (√(x))^2 = x
I thought the domain of f(g(x)) would be R, but my book said that it would be [0, infinity)
Is this because the domain of g(x) = [0, infinity), and the composite function is f(g(x))
?

Assuming the composite function exists, the domain of the entire function is the domain of the inside function. This is because you’re inserting the x values into the inside function first.
Edit: Syndicate beat me to it

[snowisawesome]

Is 2x + 3 - x^2 the same as -2x - 3 + x^2?