VCE Methods Question Thread!

[IndefatigableLover]

Let the denominator equal 0 then solve for x. The denominator of a fraction cannot be 0 as anything divided by 0 is undefined.







Therefore the domain is all real numbers excluding plus or minus 3/2.

The domain of a rational function is



Thus, the implied domain of is

Oh wow it was something that simple ._.
I can find the implied domain of other functions but that was the first quotient one I attempted so got a bit lost but thanks for all the help guys!

[Bluegirl]

I'm stuck on two questions:
Solve x for each of the following is 0 ≤ x ≤ 360, correct to the nearest tenth of a degree

3tanx°-1=3

and

Solve each of the following for x if 0 ≤ x ≤ 2∏. Find exact answers

sinx + cosx = 0

Much appreciated

[IndefatigableLover]

my previous question wasn't answered completely.

Is it possible for cubic functions(in power form) to have a dilation from y-axis?

Also (I am using a basic example here) to transform 1/x to -3/x would it be correct if I say:
You would need to reflect the graph in the y-axis?

My textbook answers says reflect in the x axis but wouldn't reflection in y-axis be the same?

Similarly, to transform 1/x to 2/x, would there be two acceptable transformations? Ie. Dilation of 2 from x OR dilation of 2 from y (since afaik, dilation of 2 really just means f(1/2x) in function notation)

-my teacher is really advanced in her teaching so I don't really understand the basics yet.

Thanks

Sorry I'm going to skip the first question because I don't know how to explain it properly...

EDIT: Yes you can have a dilation from y-axis for cubic functions.

But with your example of , when you're reflecting in the y-axis, you're essentially putting a minus sign in front of every 'x' you see in the given function. In this case you're function would be instead. If you reflect in the 'x' axis, then you essentially multiply the whole function by -1. This would be why your textbook gives you that answer

Similarly for the second one it would be a dilation of 2 from the 'x' since you're multiplying the whole function by 2 rather than substituting in a value for 'x' (like when you have a dilation of ___ from the 'y' axis'...

Hope that helps and sorry if I'm wrong (a bit rough on transformations T_T)

[Only Cheating Yourself]

already upto chapter 2? :O

We have our chapter 1 SAC this Thursday lol

Do you come to my school, lol?  Yea same here we had meth on monday and was first of school all the other classes were an introduction, i come into methods and boom.  Sac on monday.  But should be just revision as its on linear functions, whats your sac on?  And yea we're already up to chapter 2.  Also general maths compared to methods is like a glass of water and the atlantic ocean, thats the best analogy i could come up with and I'm not even kidding.

[Conic]

I'm stuck on two questions:
Solve x for each of the following is 0 ≤ x ≤ 360, correct to the nearest tenth of a degree

3tanx°-1=3

and

Solve each of the following for x if 0 ≤ x ≤ 2π. Find exact answers

sinx + cosx = 0

Much appreciated

Q1
   (Rearranging)

        (General solution)

   (using k=0 and k=1)



Q2
  (Divide both sides by cos(x), since cos(x)≠0 when sin(x)+cos(x)=0)

          (General solution)

   (Using k=1 and k=2)

[Orb]

Do you come to my school, lol?  Yea same here we had meth on monday and was first of school all the other classes were an introduction, i come into methods and boom.  Sac on monday.  But should be just revision as its on linear functions, whats your sac on?  And yea we're already up to chapter 2.  Also general maths compared to methods is like a glass of water and the atlantic ocean, thats the best analogy i could come up with and I'm not even kidding.

the first sac at my school is functions, linear relations, transformations and matrices
but we don't have ours till week 6

[Phy124]

I've got a question from the Maths Quest 11 Mathematical Methods CAS textbook. I have attached my own working out as well as the relevant pages from the textbook.

Thanks in advance for your help

Your answers are correct and in a better form than the solutions given IMO

[Bluegirl]

You really need to learn to use brackets

It didn't in the book so I didn't :/

Q1
   (Rearranging)

        (General solution)

   (using k=0 and k=1)



Q2
  (Divide both sides by cos(x), since cos(x)≠0 when sin(x)+cos(x)=0)

          (General solution)

   (Using k=1 and k=2)

Thankyou both of you

[M-D]

Thanks for that Butt124. I didn't recognize that the answer i got was the same as that given in the answers because they just looked quite different. 

[M-D]

I've got a question from the Maths Quest 11 Mathematical Methods CAS textbook. I have attached my own working out as well as the relevant pages from the textbook.

Thanks in advance for your help

Can this question be solved without using the quadratic formula?

[Yacoubb]

Hey guys

Could someone please help me with this question.

Find the derivative of each of the following with respect to x, using the product rule.

3x(2x - 1)³

I know that f'(x) = v*du/dx + u*dv/dx

so:

u = 3x
du/dx = 3
v = (2x -1)³
dv/dx = 3 * 2 * 1 * (2x -1)² = 6(2x - 1)²

dy/dx = 3x * 6(2x - 1)² + 3*(2x - 1)³
dy/dx = 18x(2x-1)² + 3(2x - 1)³

Where do I go from here? Help would be appreciated!

[Phy124]

Hey guys

Could someone please help me with this question.

Find the derivative of each of the following with respect to x, using the product rule.

3x(2x - 1)³

dy/dx = 18x(2x-1)² + 3(2x - 1)³

Where do I go from here? Help would be appreciated!

I don't see anything wrong with leaving that as your answer but you could do this:

[nhmn0301]

Can this question be solved without using the quadratic formula?

You can. Just by grouping numbers.
x^2 + 10x -8 - 20root2 = 0
( x^2 - 8 ) + 10 (x - 2root2 ) =0
( x - 2root2 ) ( x + 2root2)  + 10 (x - 2root2 ) =0
( x - 2root2 ) ( x + 2root2 + 10 ) = 0
You can solve the rest of here.
Hope this helps!

[Toki]

How do you do this question?
Sketch the graph of :
|x+4| + |x-4|
|3x+4| + |x-4|

Thanks

[b^3]

You can do it by addition of ordinates or you can do it by splitting it up into a hybrid function, I'll do the latter. Firstly lets look at each individual modulus separately.

Now remember, the modulus will  flip any part of the graph that is below the axis (so negative value), in the axis, making the value positive.



Now we need to look at which curves we have for what domain. We have three sections, the first where where both take the negative curve, where the first mod takes the positive curve and the second mod takes the negative curve, and finally where both mods take the positive curve.



Now we can plot those separate functions for the domain we have given.

See if you can try the same for the second one.