VCE Methods Question Thread!

[Daenerys Targaryen]

 

for the graph y=-[(2)/(5-3x)-1], how has it been dilated?

Dilation by factor of 2/3 from x axis

[Jaswinder]

2 from xaxis, 1/3 from yaxis?

[abcdqdxD]

Umm this is really confusing for me. Could it possibly be 1/2 from x axis 3 from y axis? 

[Wu]

Question 2, 2I in Maths Quest CAS:

Show that satisfies the equation =x+y

I've got the answer from the solutions book attached to this post but what I don't understand is why f(y) becomes 2/y. If f(y) is replaced by 2/x, why isn't the bottom one replaced either? How does it work? Why do I feel so moronic?

[availn]

Question 2, 2I in Maths Quest CAS:

Show that (Image removed from quote.) satisfies the equation (Image removed from quote.)=x+y

I've got the answer from the solutions book attached to this post but what I don't understand is why f(y) becomes 2/y. If f(y) is replaced by 2/x, why isn't the bottom one replaced either? How does it work? Why do I feel so moronic?

f is the function, and whatever is inside the brackets afterwards is substituted into the variable spot. In your case, if f(x) = 2/x, so f(3) = 2/3, f(4) = 2/4, f(a) = 2/a, f(y) = 2/y, and f(xy) = 2/(xy).

[Wu]

f is the function, and whatever is inside the brackets afterwards is substituted into the variable spot. In your case, if f(x) = 2/x, so f(3) = 2/3, f(4) = 2/4, f(a) = 2/a, f(y) = 2/y, and f(xy) = 2/(xy).

Thank you for your clear explanation. I am now up to the second step.

I went about the next part by cross multiplying 2/x+2/y which would get me 2y+2x but I understand that it should be divided by xy. Is this because I am meant to be adding these adding algebraic functions together like a/c+a/b=a+b/c? (because if the latter, I have never been taught this before.)

[abcdqd]

Umm this is really confusing for me. Could it possibly be 1/2 from x axis 3 from y axis? 

no

[abcdqdxD]

no

nvm i figured it out

[b^3]

Thank you for your clear explanation. I am now up to the second step.

I went about the next part by cross multiplying 2/x+2/y which would get me 2y+2x but I understand that it should be divided by xy. Is this because I am meant to be adding these adding algebraic functions together like a/c+a/b=a+b/c? (because if the latter, I have never been taught this before.)

We have . To combine them into one fraction, we need to have them over the same denominator. So we need to multiply both by 'something/something' to get the same denominator, but to keep everything equal, what we multiply the top by we must multiply the bottom by, as this is effectively multiplying by 1. So in our case we will multiply the first fraction by and the second fraction by . That gives

With the link you have, you haven't stated exactly what is given in the link, you've given different denominators, but we have the same denominators so we can just add the numerators together.

[Daenerys Targaryen]

Consider and . What transformations are required to obtain from ?

[e^1]

Consider and . What transformations are required to obtain from ?

Convert it into matrix form (if you like, I'm only using it to show the transformations):








As we can see, to get from to , we need to change the values of: dilation from y-axis and the horizontal translation (since both are not the same).

Firstly, we can see that there is a reflection in the y-axis, from comparing the matrices (from 1 to -1).

Now, to find the horizontal translation, we should see what happens when we apply this reflection to . It then becomes . Hence, to get to , we would need a horizontal translation of 1 unit to the right.



Here is another way of seeing it:



EDIT: corrected.

[Daenerys Targaryen]

Convert it into matrix form:








As we can see, to get from to , we need to change the values of: dilation from y-axis and the horizontal translation (since both are not the same).

To get from 4 to -3, we need a horizontal translation of 7 units to the left.
To get the dilation from the y-axis, from 1 to -1, then we would add a dilation from the y-axis by a factor of -1 (or a reflection in the x-axis).


Hence these are the translations that we need to get from to .

Yeah sweet, this is what i had; the text book answer said:
'Reflection in the y-axis, translated +1 parallel to the x-axis'
So dilation -1 same as reflection; but that +1 parallel isn't the same as left 7 which was what i got..

[swampman]

Let f: R-->R, f(x) = squareroot(4-x^2) and S be the set of all real values of x for which f(x) is defined. Let g:R-->R, where g(x)= x^2+1

How do I find S?

Thanks!

[Daenerys Targaryen]

Let f: R-->R, f(x) = squareroot(4-x^2) and S be the set of all real values of x for which f(x) is defined. Let g:R-->R, where g(x)= x^2+1

How do I find S?

Thanks!

Wouldn't that be just the Domain of f(x)?

[swampman]

omg haha yes, i worked it out xD ( sorry that was silly)