Functions and Transformations.. one step at a time..

Alive · 2011-03-01 13:24:28

Could you please explain what dilation, reflection, translation are in transformations.

There are questions like:

y = 2(x+1)^3 - 6

1) Find the stationary point of inflection
2)State the transformation that the graph y=x^3 has undergone to produce the given graph
3) State the transformation(s) that the graph y=x^3 has undergone to produce the given graph.

SO basically what is a stationary point of inflection??

Then there is the HYPERBOLA
There are questions like: Sketch the graph of
y= (2/x+2) - 4
clearly showing the intercepts with the axes and the position of the asymptotes.

SO how do we find out the asymptotes?

y = (2/5) + (4/1+x)
Also find the asymptotes and the intercepts with the axes.

Then there is the TRUNCUS...

1. y = 4 - ( 2/(3+x) ^2)

Clearly state the position of the asymptotes and the intercepts with the axes (correct to 1 decimal place where appropriate)

Then there is the SQUARE ROOT FUNCTION IN POWER FORM

y = -3/5 √3x-4+2

After this there's the absoolute value function, transformations with matrices, sum difference and prooduct functions, composite functions and functional equations AND MODELLING)...

But right now I must know the way to the questions above. I know it might be long but the teacher wants us to know these urgently as he is going to proceed to more advanced questions. Please could you explain the basic principles and the way to do these. There's so much more questions but I will need to know these. Like the Domain, Range, Point of inflection, x-y intercepts, transformations.... There's a lot of questions that also need rearranging which I have no clue to how to do it. I know it need basic algebra for some but I don't have time to review, I need to learn all at once... So it's like algebra and advanced algebra at once. So please help me out (urgently)

bobbym · 2011-03-01 17:35:28

Hi Alive;

There is a whole lot of questions up there! Go here for the first one.

http://www.mathsisfun.com/geometry/transformations.html

For the asymptotes, I think you had some help on that before:

http://www.mathisfunforum.com/viewtopic.php?id=14369

Alive · 2011-03-01 20:36:16

2(x+1)^3 - 6

So it's going to be positive so no reflection. Dilation of 2 which means how much it lengthens. -1 to the left. ^3 means cubic graph? -6 units down?
The stationary point of inflection is (-1,-6).

(2/x+2) - 4

So basically 2 is the dilation right? -2 then should be -2 in the x axis? -4 units down? So only in a hyperbola, a asymptote is the y=c and x=b? So asymptotes x=-2; y=-4. We find y intercept by... y-int: x=0
y=( 2/0+2) -4 = -3. Point (0,-3).
Now we find x intercept. 0=2/(x+2) -4
4=2/(x+2)
4(x+2) = 2
4x+8=2
4x=-6
x=-6/4
x=-3/2
Point (-3/2,0)

(2/5) + (4/1+x)
I have no idea? I'm not so good with these kind of things. Do we need to re arrange, if so how? Do you have any worksheets or a website for these kinds of questions. I'm not really good at re arranging things?

y = 4 - ( 2/(3+x) ^2)
So which one is the dilation?? where do we start for this one?

y = -3/5 √(3x-4) +2
End point is (4,2)
x int.: 0=-3/5 √(3x-4) +2
-2 = -3/5√(3x-4)
What next? Again i'm not so good at these kinds of things.. If you have any worksheets of this, it will be great as knowing the basics will help the workout going.

bobbym · 2011-03-01 21:39:44

Hi Alive;

y = ( 2/0+2) -4 = -3.

That does not equal -3

Alive · 2011-03-01 21:44:36

Oh, I meant (2/0+2) -4
= -3.

Could you help me with the other questions I asked please.

bobbym · 2011-03-01 21:47:34

Hi;

That is still not bracketed right. 2 / (0 +2) - 4 = -3.

Is that function this:

Alive · 2011-03-01 21:49:53

Yes it is.

bobbym · 2011-03-01 21:54:28

For that one you are correct. y intercept = -3 and x intercept or root = 0.

Alive · 2011-03-01 22:02:54

Do you know how to do the rest... this is kind of urgent as there are more advanced questions.

bobbym · 2011-03-01 22:05:46

Hi Alive;

There is a lot of work up there and it is difficult to understand your formatting. I will do as many and as much as I can. Does the next one look like this?

Alive · 2011-03-01 22:12:09

Yes except the x+3 is 3+x... but you can re-arrange it I suppose..?
And how do you put the question in that format.

bobbym · 2011-03-01 22:17:58

That is the y intercept.

Alive · 2011-03-01 22:26:21

Okay.. so the domain and range is needed..

Bob · 2011-03-01 22:33:39

hi Alive

And how do you put the question in that format.

bobbym is using a computer language called LaTex.

If you click on one of the bits of his post you'll see the code.

You have to start with square bracket math to switch the LaTex interpreter on and finish with square brackets /math

Bob

bobbym · 2011-03-01 22:40:22

Hold it. The x intercept or the root is needed.

Expand and solve.

Alive · 2011-03-01 23:33:09

How did you expand that..?

And I tried the format, it worked, thanks

Last edited by Alive (2011-03-01 23:34:58)

bobbym · 2011-03-01 23:44:08

Hi Alive;

Do you remember FOIL for expanding a binomial term?

Alive · 2011-03-01 23:49:36

Yeah but I get:

0 = 4(x^2 + 6x + 9) -2
0 = 4x^2 + 24x + 36 - 2...
0 = 4x^2 + 24x + 34
-4x^2 = 24x + 34
??

bobbym · 2011-03-01 23:52:29

Why bring that 4x^2 to the other side. Leave it the way it is and use the quadratic formula.

Alive · 2011-03-02 00:05:41

(-24 +- √24^2 - 4(4)(34)) /8
(-24 +- √576-544) /8
(-24 +- √26) /8
???
I'm not so used to the Quadratic Formula

Last edited by Alive (2011-03-02 00:06:11)

bobbym · 2011-03-02 00:11:33

for:

Can you finish now?

Alive · 2011-03-02 00:20:32

(-24 +√26) /8
(-24 - √26) /8

I don't know how to solve these... Square roots etc.? so 2 and 13 go into 26...? 24 and 8 can be divided by 8...

bobbym · 2011-03-02 00:38:26

Hi Alive;

I am not getting that 26 under the square root sign. Please check your calculations again.

Alive · 2011-03-02 00:47:59

Okay so it was 32.... 4x4x2 makes the 32... 4√2 ?
-24 + 4√2
-----------------
8

Can you please solve this. I don't know the steps for this..??

bobbym · 2011-03-02 00:56:34

Hi Alive;

You have to be neater in your presentation. That is very hard to read.

you have 2 answers:

Every number in that fraction is divisible by 4. So divide each number by 4.

The next one is:

Every number in that fraction is divisible by 4. So divide each number by 4.

Math Is Fun Forum

#1 2011-03-01 13:24:28

Functions and Transformations.. one step at a time..

#2 2011-03-01 17:35:28

Re: Functions and Transformations.. one step at a time..

#3 2011-03-01 20:36:16

Re: Functions and Transformations.. one step at a time..

#4 2011-03-01 21:39:44

Re: Functions and Transformations.. one step at a time..

#5 2011-03-01 21:44:36

Re: Functions and Transformations.. one step at a time..

#6 2011-03-01 21:47:34

Re: Functions and Transformations.. one step at a time..

#7 2011-03-01 21:49:53

Re: Functions and Transformations.. one step at a time..

#8 2011-03-01 21:54:28

Re: Functions and Transformations.. one step at a time..

#9 2011-03-01 22:02:54

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#10 2011-03-01 22:05:46

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#11 2011-03-01 22:12:09

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#12 2011-03-01 22:17:58

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#13 2011-03-01 22:26:21

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#14 2011-03-01 22:33:39

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#15 2011-03-01 22:40:22

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#16 2011-03-01 23:33:09

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#17 2011-03-01 23:44:08

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#18 2011-03-01 23:49:36

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#19 2011-03-01 23:52:29

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#20 2011-03-02 00:05:41

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#21 2011-03-02 00:11:33

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#22 2011-03-02 00:20:32

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#23 2011-03-02 00:38:26

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#24 2011-03-02 00:47:59

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#25 2011-03-02 00:56:34

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