Functions

[bucket]

Don't know about the topic heading, modify it if it's not right (I try to make my topics broad so if others has a question relating to the topic the board isn't spammed with millions of threads.)

Anyway... I have two separate questions regarding dilation, fairly simple but I don't understand when my teacher explains.
State a transformation which maps the graphs of to for:
1.

2.






(i had to modify because i wrote the question wrong)

[enwiabe]

Step 1: Raise (x^-2) to the power of -1/2
Step 2: Dilate parallel to the y-axis by a factor of sqrt(5)

[bucket]

Step 1: Raise (x^-2) to the power of -1/2
Step 2: Dilate parallel to the y-axis by a factor of sqrt(5)

mm these are two seperate questions

[enwiabe]

Nooo, one question, two equations.

[bucket]

oh i guess ive written them wrong then lol, i think i joined two seperate questions! sec ill modify

[Collin Li]

The first one is a dilation parallel to the y-axis by a factor of 5.

The second one should be , I assume, and that is a dilation parallel to the x-axis by a factor of 1/5.


About your LaTeX coding:

Code: [Select]

\sqrt{5x}
Nets you:

If you neglect the curly brackets, with this code:

Code: [Select]

\sqrt 5x
You get:

[Collin Li]

Also, here is the general syntax for transformations:



* If , then there is a reflection in the x-axis
* If , then there is a reflection in the y-axis

* Dilation parallel to the y-axis (or "from the x-axis") by a factor of
* Dilation parallel to the x-axis (or "from the y-axis") by a factor of
* Translation in the positive direction of the x-axis by units
* Translation in the positive direction of the y-axis by units

NOTE: You should list your transformations in the correct order: make sure you do reflections and dilations before you do translations (otherwise your translation will become reflected and translated as well). Basically, translations last!

[Mao]

coblin i thought it was following this pattern if was horizontal translation:

[Collin Li]

coblin i thought it was following this pattern if was horizontal translation:

Hmm... you are right! Fixed now, thanks

[lanvins]

how would u reflect y =3x^2+ 2x +14 in the y axis and how would u reflect it in the x axis? i know what it looks like when you graph it, i just don't know how to write it.

why does 3x^2+ 2x +14 get smaller when i do 3(-x)^2 + 2(-x) +14?

would it be okay to describe (2x^2) as a dilation of a factor of 2 from the x axis?

Would u describe the transformations of the graph 1/(4-3x)^2 +1 as
1. a dilation from the y axis by a factor of 1/3
2. Then a reflection in the y-axis
3. Then a translation of 4 in the negative direction of the x
4. Then a translation of 1 in the positive direction of the y axis?

thanks

[unknown id]

"how would u reflect y =3x^2+ 2x +14 in the y axis and how would u reflect it in the x axis? i know what it looks like when you graph it, i just don't know how to write it."

reflect in the x-axis:
-f(x) = -(3x^2+ 2x +14)
       = -3x^2 -2x -14

reflect in the y-axis:
f(-x) = 3(-x)^2 + 2(-x) + 14
       = 3x^2 -2x + 14

[unknown id]

"would it be okay to describe (2x^2) as a dilation of a factor of 2 from the x axis?"

yea, that would be okay. To get from f(x)= x^2 to g(x)= 2x^2, a dilation of a factor of 2 from the x-axis/in the y-direction is required.

[unknown id]

"Would u describe the transformations of the graph 1/(4-3x)^2 +1 as
1. a dilation from the y axis by a factor of 1/3
2. Then a reflection in the y-axis
3. Then a translation of 4 in the negative direction of the x
4. Then a translation of 1 in the positive direction of the y axis?"

Your steps 1,2 and 4 are all correct. However for step 3, what is required is "Then a translation of *4/3 units in the *positive direction of the x"

This is because you have to make the denominator of the fraction equal to zero:
(4-3x)^2 = 0
4-3x = 0
x = 4/3

[lanvins]

thanks unknown id,
one more question, why does putting the power sign in brackets affect whether its reflected in the y or x axis. for example (-x^2) and (-x)^2

[unknown id]

The power sign does not affect whether a function is reflected in the x- or y-axis.

Like I said before, when it asks to reflect f(x) in the x-axis, the new function g(x) will equal to
-f(x).

When it asks to reflect f(x) in the y-axis, the new function h(x) will equal to
f(-x). Hence the power sign should be outside the brackets.