VCE Methods Question Thread!

[TheCommando]

For each of the following, state a transformation which maps the graph of y=f(x) to the graph of y=f1(x):

a)f(x)=x2, f1(x)=(x+5)^2

Can someone please break this down and explain?

Or i just say
There is a shift of factor 5 in the negative direction of the x axis
And thats just by identifying the +5 in the brackets squared

[TheCommando]

Two ways to do this one; both are pretty much the same.

1. Draw a triangle and use pythagoras theorem (this question is very easy if you notice it's a pythagorean triad: 3-4-5)

2. Use the distance formula, sub in your values and solve algebraically. \(D = \sqrt{(x_2 - x_1)^2 + (y_2 + y_1)^2}\). This will give you \(5 = \sqrt{(5-2)^2 + (y+1)^2}\). Doing this you might end up with only \(y=3\), but it's important to note that \(y=-5\) is an equally valid answer. If you only get one answer, you need to go back and consider that \(y\) is to the power of two, so there will be two solutions.

Let me know if I wasn't clear enough, or you would like a line by line solution.

How do u know y is the power of 2

[LPadlan]

Two ways to do this one; both are pretty much the same.

1. Draw a triangle and use pythagoras theorem (this question is very easy if you notice it's a pythagorean triad: 3-4-5)

2. Use the distance formula, sub in your values and solve algebraically. \(D = \sqrt{(x_2 - x_1)^2 + (y_2 + y_1)^2}\). This will give you \(5 = \sqrt{(5-2)^2 + (y+1)^2}\). Doing this you might end up with only \(y=3\), but it's important to note that \(y=-5\) is an equally valid answer. If you only get one answer, you need to go back and consider that \(y\) is to the power of two, so there will be two solutions.

Let me know if I wasn't clear enough, or you would like a line by line solution.

Hey, can you please do a line by line solution? i didn't see this reply previously. Thanks

[zhen]

I know how to do these questions but i dont particularly understand these concepts as the book explanation is very brief and doesnt explain it.
So why is -sin (pie/2 - theta) =a= cos theta
- cos(pie/2 -theta)= b =sin theta
Why is sin (pie/2 + theta)=a =cos theta
Cos (pie/2 +theta) =-b =-sin theta

Pretty sure the first one is wrong. -sin(π/2-θ)=-cos(θ), since sin(π/2-θ) is in the first quadrant and is positive, so the negative of it would be negative.
-cos(π/2-θ)=-sin(θ), similar to first one
sin(π/2+θ) is in the second quadrant which is positive for sine. So sin(π/2+θ)=cos(θ)
cos(π/2+θ) is in the second quadrant, which is negative for cosine, so it's -sin(θ)

This image explains why these identities work if you want to understand it,
Also someone should correct me if I got anything wrong, since I may have made a mistake, which may be why I got a different answer to you.

[zhen]

Hey, can you please do a line by line solution? i didn't see this reply previously. Thanks

Here's my line by line solution. Hope it helps.

[TheCommando]

Pretty sure the first one is wrong. -sin(π/2-θ)=-cos(θ), since sin(π/2-θ) is in the first quadrant and is positive, so the negative of it would be negative.
-cos(π/2-θ)=-sin(θ), similar to first one
sin(π/2+θ) is in the second quadrant which is positive for sine. So sin(π/2+θ)=cos(θ)
cos(π/2+θ) is in the second quadrant, which is negative for cosine, so it's -sin(θ)

This image explains why these identities work if you want to understand it,
Also someone should correct me if I got anything wrong, since I may have made a mistake, which may be why I got a different answer to you.

They all all meant to be positive
That - was simply meant to show a list my bad. Thank you for helping and will read in the morning

[dylang99]

state the transformations required to map the graph of y=f(x) onto the graph of y = F(X/N) + K. If there is a turning point at (2,3), Find all the possible values of n and k. Sketch the corresponding graphs

[LPadlan]

Find the matrix that determines the composition of following transformations, in the given order, and find the image of the point(-3,2) under this transformation:
-reflection in the x-axis
-dilation of factor 2 from the x-axis

[QueenSmarty]

Find the matrix that determines the composition of following transformations, in the given order, and find the image of the point(-3,2) under this transformation:
-reflection in the x-axis
-dilation of factor 2 from the x-axis

Let A= matrix for reflection in x-axis and B= matrix for dilation of factor 2 from x-axis
A= [1  0]     B= [1 0]
      [0 -1]          [0 2]
BA= [1  0]  [1   0]      [1  0]
        [0  2]x[0  -1]   = [0 -2]
Image of (-3, 2) under the transformations: BA [-3]     [1   0]     [-3]     [-3]
                                                                          [ 2 ] =  [ 0 -2] x  [2 ] =  [-4]
Therefore, the answer is (-3, -4)
                                     

[Syndicate]

state the transformations required to map the graph of y=f(x) onto the graph of y = F(X/N) + K. If there is a turning point at (2,3), Find all the possible values of n and k. Sketch the corresponding graphs

Is the type of graph (ie. quadratic, cubic etc...) listed above the question?

[LPadlan]

For h(x)=81x^4-72x^2+16, find the coordinates of the points where the graph of y=h(x) intersects the x and y axes, and hence sketch the graph

[cookiedream]

For h(x)=81x^4-72x^2+16, find the coordinates of the points where the graph of y=h(x) intersects the x and y axes, and hence sketch the graph

Here's my worked solutions

[TheCommando]

Hi i dont understand the explanations of how they did this question like get the solution for theta =pie/6
Ps why cant i attach the image. It says my image is way to big wtf
https://postimg.org/image/g2xhv8789/

[TheCommando]

Pretty sure the first one is wrong. -sin(π/2-θ)=-cos(θ), since sin(π/2-θ) is in the first quadrant and is positive, so the negative of it would be negative.
-cos(π/2-θ)=-sin(θ), similar to first one
sin(π/2+θ) is in the second quadrant which is positive for sine. So sin(π/2+θ)=cos(θ)
cos(π/2+θ) is in the second quadrant, which is negative for cosine, so it's -sin(θ)

This image explains why these identities work if you want to understand it,
Also someone should correct me if I got anything wrong, since I may have made a mistake, which may be why I got a different answer to you.

yeah i dont get that......
Ill ask my tutor
I watched khanacademy video and i understood it put it was different
[img]https://s23.postimg.org/8z5ohysyv/IMG_9915.png[/img]

[Syndicate]

Hi i dont understand the explanations of how they did this question like get the solution for theta =pie/6
Ps why cant i attach the image. It says my image is way to big wtf
https://postimg.org/image/g2xhv8789/

These are exact values. You need to memorise them.