VCE Methods Question Thread!

[CarrymetoUni]

So, I've done this question and my order of transformations were right, however I stated my translation as "7 units in the positive direction of y axis" while the textbook had it as "7/3 in the positive direction of y-axis". Could any of you math geniuses explain to me why my answer is different?

[Shadowxo]

So, I've done this question and my order of transformations were right, however I stated my translation as "7 units in the positive direction of y axis" while the textbook had it as "7/3 in the positive direction of y-axis". Could any of you math geniuses explain to me why my answer is different?

Well there are two different ways to do it
Either you go up 7, then dilate it by a factor of 1/3 from x axis
y=3(3x+1)²-7
=> y = 3(3x+1)²
=> y = (3x+1)²

or you could dilate by a factor of 1/3 from x axis then go up 7/3
y=3(3x+1)²-7
=> y=(3x+1)²-7/3
=> y=(3x+1)²

There are two different approaches that both result in the same answer, but if you dilate by a factor of 1/3 first, you then need to go up 7/3 instead of 7

[Sine]

Whenever you have to state transformations to go from a complex function to a basic function.

For example something like to

Do the translations first then reflections/dilations makes it much easier and also reduces the chance of making a silly mistake

[noregret]

Hello, I have a test tommorow next week about transformations and I cannot understand the dilation from the y-axis. My teacher wrote if the function is dilated by a function of n in the x-direction, replace x with x/n but this does not work in every situations. For example it does not work in this equation: graph of y=1/x^2 has been dilated by a factor of 3 from the y-axis. Can someone give a clear explanation of a dilation frim the y-axis without using any matrices or textbook explanation (because he does not want the class to use those methods).

[Shadowxo]

Hello, I have a test tommorow next week about transformations and I cannot understand the dilation from the y-axis. My teacher wrote if the function is dilated by a function of n in the x-direction, replace x with x/n but this does not work in every situations. For example it does not work in this equation: graph of y=1/x^2 has been dilated by a factor of 3 from the y-axis. Can someone give a clear explanation of a dilation frim the y-axis without using any matrices or textbook explanation (because he does not want the class to use those methods).

I'll explain it as best I can
Also - it should work in every situation. eg -

This is dilated by a factor of 3 from the y axis - in this case it's also the same as dilating by a factor of 9 from x axis.

So, If a graph is dilated from the y axis by a factor of n, see the y axis and imagine the graph being pulled closer to or further away from it. If it's dilated by, for example, a factor of two, you stretch it out further away from the y axis, so the new x value is twice as much as the original x value.
In this scenario, the y value stays the same and the x value doubles. In order for the y value to stay the same, you need to divide the new x value by 2 in order to keep the same y value. So you change x to x/2 if you dilate it by a factor of 2 from the y axis, so the new y value is the same as the old y value when x is double what it originally was, aka x has to be twice as large for the same y value to occur.
so, when dilating from the y axis by a factor of n, you replace x with (x/n), so when x is n times the original value, the y value stays the same

Does this help a bit?

[noregret]

Thanks for your reply, there is one more question I want to ask you, If the graph of y=1/x^2 has been dilated by a factor of 3 from the y-axis is equal to y=1/(x/3)^2, then how come if the graph of 1/x has been dilated by a factor of 3 from the y-axis equals to y=1/x/1/3=y=3/x?

[vcestressed]

Hey,
I am dying bc of this question so can someone please pls help...
How many kg of brand X coffee which costs $24.80/kg must be added to 5.6 kg of brand Y coffee which costs $20.90/kg to make Jaidee's special coffee blend which costs $22.40/kg?
Thank you!!!

[peanut]

Thanks for your reply, there is one more question I want to ask you, If the graph of y=1/x^2 has been dilated by a factor of 3 from the y-axis is equal to y=1/(x/3)^2, then how come if the graph of 1/x has been dilated by a factor of 3 from the y-axis equals to y=1/x/1/3=y=3/x?

y = 1/x is an odd function, so dilation by a factor of 3 from the y-axis is the same as dilation by a factor 3 from the x-axis. This doesn't apply to y = 1/(x^2) as that function is even, not odd.

[Shadowxo]

Thanks for your reply, there is one more question I want to ask you, If the graph of y=1/x^2 has been dilated by a factor of 3 from the y-axis is equal to y=1/(x/3)^2, then how come if the graph of 1/x has been dilated by a factor of 3 from the y-axis equals to y=1/x/1/3=y=3/x?

I'm not entirely sure of your question, but even though the graphs of y=1/x and y=1/x² look similar from 0 to infinity, they're different, as one is squared. So even though they're dilated the same amount from the y axis, it'll be a different amount from the x axis as they're different graphs. https://www.desmos.com/calculator might help a bit to be able to see and compare the different graphs

Hey,
I am dying bc of this question so can someone please pls help...
How many kg of brand X coffee which costs $24.80/kg must be added to 5.6 kg of brand Y coffee which costs $20.90/kg to make Jaidee's special coffee blend which costs $22.40/kg?
Thank you!!!

It's like an average of the two, but taking into account proportions


Alternatively, the cost of X plus the cost of Y is equal to the cost of (amount of x + amount of y)* new price

[LPadlan]

b/x-a = 2b/x+a solve for x

[Shadowxo]

b/x-a = 2b/x+a solve for x

Or if it's this question

[deStudent]

http://m.imgur.com/a/Dby1Y

How did the answer get a factor of "-1/3" out in the front?

Ty

[Sine]

http://m.imgur.com/a/Dby1Y

How did the answer get a factor of "-1/3" out in the front?

Ty

they got the answer wrong

back yourself 

For the book to be correct the extra step would be a dilation of scalar factor 1/3 from the x-axis

[Mehul123]

How do you graph inverse functions in  math methods 1/2

[Escobar]

How do you graph inverse functions in  math methods 1/2

either 1. find the inverse function by swapping x and y in the original function and isolating y
or 2. reflect the original function over the line y=x