Dilation of X and Y axis? So confusing!

[kenhung123]

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For a given function such as cirular, parabolae, hyberbolae and cubic what is the difference between dilation on x and y axis?

I only know that dilation on x is the change in y value and dilation on y is change in x value.

How does the graph shape change? How do you identify the dilation factor and the axis without a given graph?

I also remember that somehow when dilating on y axis by 3, the factor is 1/3 for parabolic functions?

Please help! This is such a basic yet confusing concept!

[Spluff]

Dilation parallel to the x is the reciprocal of the coefficient (ie. 3 becomes 1/3) and given within the function. ie. y=cos(3x) is dilated by a factor of 1/3 parallel to the x axis (also written as away from the y axis - just think of it as horizontally).

Other dilations by a factor of 1/3 parallel to the x axis are:

y=e^(3x), y=(3x)^2, y=1/(3x)

Dilation parallel to the y axis (vertical) are given outside the function. ie. 3sin(x) is dilated by a factor of 3 parallel to the y axis.

Other dilations by a factor of 3 parallel to the y axis are

y=3e^x, y=3x^2, y=3/x (or y=3(1/x)).

The graphs change shape by stretching (or contracting) in the direction of their dilation. ie. a graph dilated by a factor of 3 parallel to the y axis becomes 3 times taller.



Hopefully this helps.

[kenhung123]

Sorry but when you refer 'parallel to the x/y axis' does that mean x/y axis dilation respectively?

[Brentos_Milk]

I too am super confused with dilations.
On the Heffernan 2006 exam 1, question 7, the graph changes from 1/X to 4/X and the question asks you to describe the transformation that takes place. Going by what Spluff says, the answer should be a dilations of 4 parallel to the y-axis shouldn't it? But the answer is 4 parallel to the X axis or 4 away from the Y-axis.
So who's wrong? Could someone refer me to some sort of reference that explains dilations because I can't find them in my text book.

Thanks

[samaccount123]

This is equivelent to extension 1 or 3 unit maths in NSW..so IDK..and I did 2 unit

[M3rC]

apparently the VCAA set the standard as "from x/y"
so, we dont have to learn the countless number of ways in which the transformations can be applied such as "parallel to/in the X-direction/vertical dilation"
and all that crap, i'm not 100% sure.

but i've been told the standard was set as "FROM X or Y"

[Cobalt]

Dilation from x/y is the same as dilation parallel to y/x respectively.

[pineapplebaby]

Originally Posted by Brentos_Milk

I too am super confused with dilations.
On the Heffernan 2006 exam 1, question 7, the graph changes from 1/X to 4/X and the question asks you to describe the transformation that takes place. Going by what Spluff says, the answer should be a dilations of 4 parallel to the y-axis shouldn't it? But the answer is 4 parallel to the X axis or 4 away from the Y-axis.
So who's wrong? Could someone refer me to some sort of reference that explains dilations because I can't find them in my text book.

Thanks

eg, dilation of 3 on the x-axis: multiply 3 with the entire function, aka, f(x) or whatever they give you.

dilation of 3 on the y-axis: f(1/3)--so you always flip the whole number.

Therefore, in response to the q from Heffernan, f(x)=1/X ----> 4f(x)=4/x, therefore dilation of 4 from the x-axis.

Remember, dilation from the x-axis is a vertical dilation (streches up-down so its the y value or f(x) that changes, therefore multiplying dilation with f(x).


Hope that helps.

[Vce121]

Transformation Description of effect,

f(-x) Reflection about the y-axis (flip around)
-f(x) Reflection about the x-axis (flip over)
f(x+h) Translation h units in the negative direction, parallel to x-axis
f(x-h) Translation h units in the positive direction, parallel to x-axis
f(x)+h Translation k units in the positive direction, parallel to x-axis
af(x) Dilation factor of a, parallel to y-axis (from x-axis)
f(ax) Dilation factor of , parallel to x-axis(from the y-axis)
f(1/x) Dilation factor of a, parallel to x-axis (from y axis)

I have a chart which helps me remember

hope this helps.

[Multihunter]

Originally Posted by Vce121

Transformation Description of effect,

f(-x) Reflection about the y-axis (flip around)
-f(x) Reflection about the x-axis (flip over)
f(x+h) Translation h units in the negative direction, parallel to x-axis
f(x-h) Translation h units in the positive direction, parallel to x-axis
f(x)+h Translation k units in the positive direction, parallel to x-axis
af(x) Dilation factor of a, parallel to y-axis (from x-axis)
f(ax) Dilation factor of , parallel to x-axis(from the y-axis)
f(1/x) Dilation factor of a, parallel to x-axis (from y axis)

I have a chart which helps me remember

hope this helps.

ummm... can you plz check those last two... 'cause they don't make sense....

[Vce121]

Originally Posted by Multihunter

ummm... can you plz check those last two... 'cause they don't make sense....

Transformation Description of effect,

f(-x) Reflection about the y-axis (flip around)
-f(x) Reflection about the x-axis (flip over)
f(x+h) Translation h units in the negative direction, parallel to x-axis
f(x-h) Translation h units in the positive direction, parallel to x-axis
f(x)+h Translation k units in the positive direction, parallel to x-axis
af(x) Dilation factor of a, parallel to y-axis (from x-axis)
f(ax) Dilation factor of 1/a, parallel to x-axis(from the y-axis)
f(1/x) Dilation factor of a, parallel to x-axis (from y axis)

I have a chart which helps me remember

hope this helps.

Sorry i copied it from a word sheet.

[M3rC]

Just a quick question;
If we dilate from the y-axis (parallel to Y) would that affect the implied domain?

Because dilating FROM the X-AXIS obviously changes the range of that function...so would the same apply for the x-axis when dilating parallel to y?

Argh, that does my head in and noone can give me a straight, solid answer

[Spluff]

Originally Posted by M3rC

Just a quick question;
If we dilate from the y-axis (parallel to Y) would that affect the implied domain?

Because dilating FROM the X-AXIS obviously changes the range of that function...so would the same apply for the x-axis when dilating parallel to y?

Argh, that does my head in and noone can give me a straight, solid answer

I think you've got your wires crossed, dilating from the y-axis is parallel to x, not parallel to y.

Dilating from y axis, (parallel to x) will change the implied domain, but it will not change the range.

Dilating from the x axis (parallel to the y) will not change the implied domain, but will change the range.

[M3rC]

Whoops, yeah that's what i meant.
Thanks Spluff!