Question

Please help me somebody! Thank you! :)

Answer 1

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Answer 2

compressed, because the bigger the number (a), in a(x^2), the narrower the graph gets

Answer 3

Hello, Mark! Looks like you h ave a significant graphing exercise ahead of you. If you're learning this material for the first time, graphing every function, comparing it to the parent function and describing the differences is the way to go.

Answer 4

try it on a calculator

Answer 5

use a TI or something, and compare the graphs

Answer 6

alright, ill use desmos online.

Answer 7

Mathmale I learned this stuff before, but the thing is I didn't really care for it back then so now I am trying very hard to understand these things. :)

Answer 8

That's another way to go. It just occurred to me that if you were to graph 2 functions on a TI calculator simultaneously, the comparison would be simpler.

Answer 9

ah I see.

Answer 10

I'm not very familiar with Desmos. It'd be neat were you able to graph 2 different functions on the same set of axes.

Answer 11

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Answer 12

keep in mind that you can plug in numbers as well and try to mentally visualize what's going on - I like graphing applications, but oftentimes on math tests you're not allowed usage of powerful calculators or even regular ones

Answer 13

I agree that graphing skills (the manual kind) are of great importance despite the ready availability of technology. But I don't have any problem with using tech here to compare the graphs of several different versions of y=x^2. You, Mark, decide which path you want to take and what kind of help you need and want.

Answer 14

Ok so I think its a veritcal compression, but im not sure by what number. :(

Answer 15

@mathmale

Answer 16

ahh never mind I think I got it. Is it a vertical compression of 1/b?

Answer 17

Mark: You have several versions of two different functions here. Be sure to mention which one you're focusing on.

Parent function y=x^2 has a graph which is a parabola that opens upward.
1st modification is y=(2x)^2 , or y=4x^2. How is the graph of this modification different from that of the original function?
2nd mod is y=(3x)^2 ....
3rd mod is y=(4x)^2.

You need to determine how the graph changes as you move from one of these to the next one.

Answer 18

No vertical compression here (at least not in the case where the parent function is y=x^2).

Are you willing to graph these functions or are you going to try to swing it without doing any graphing?

Answer 19

The general form of this function would be y= (cx)^2. Can you finish this sentence?

"When c is a positive number greater than 1, the graph of y=(cx)^2 differs from that of the graph of y=x^2 in that .... ???? "

Answer 20

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Answer 21

Glad you are making progress. But I see you're not (yet) answering any of my comments or questions.

Answer 22

lol yea shas I will get back to you im sorry I just noticed the questions. Didn't mean to be rude. :(

Answer 23

the thing is this assignment expires or times out after a while and I have to redo it all over again. :(

Answer 24

Guess it's a matter of 1) finishing the assignment in a hurry but not learning much from the experience, or (2) learning from the experience even if it takes longer. Your choice.

Answer 25

Yes, I understand your concern. The thing is I am saving my questions up. I will be back to understand it better. But for now I have to finish. :)

Answer 26

on my last one.

Answer 27

In general, if you have a function of the form y=f(x), (1) multiplying x by a positive number will cause HORIZ COMPRESSion of the graph. (2) mult x by a fraction between (0 and 1 ) will cause HORIZ EXPANSION. You could verify these rules for your self if you wish by doing experiments.

Answer 28

ok im back. :)

Answer 29

Well, then, what kind of help do you want with the last one, other than the answer itself? ;)

Answer 30

I knew about the compression part, but I wanted to know the number itself being compressed. If you may help me understand that part.

Answer 31

Note that the last sentence of your homework assignment here says the same thing as I shared with you 2 minutes ago.
My comment was general: "horiz. compression." You apparently want something more specific, e. g., "horiz compress. by a factor of so and so."

Let's learn by example. Suppose b is 2. The original graph will be horiz. compr. by a factor of what?

Answer 32

1/2

Answer 33

To test your knowledge:

The period of the sine function (of the form y=sin x) is 2pi.

What is the period of the sine function y=sin 3x? What is b?

Answer 34

Yes, 1/2 was correct, for your previous problem.

Answer 35

Yes! :)

Answer 36

:)

Answer 37

The period of y=sin 3x is .... ?

Answer 38

1/3x?

Answer 39

Note that the graph of y=sin 3x is horiz. compressed when compared to the graph of y=sin x.

Explain. Why have you included x in your most recent result?

Answer 40

To test your knowledge:

The period of the sine function (of the form y=sin x) is 2pi.

What is the period of the sine function y=sin 3x? What is b?

Answer 41

Idk I just did an educated guess lol.

Answer 42

aha so 2pi*3

Answer 43

You tell me: if we start with y=f(x) and replace x with cx, and c is a positive constant greater than 1, how is the graph of y=f(cx) different from that of y=f(x)?

Answer 44

Right. The period of y=sin x is 2pi, and so the period of y=sin 3x is 2pi/b, or 2pi/3. Bingo.

Answer 45

What is the period of y=sin (1/4)x?

Answer 46

4?

Answer 47

not correct im guessing. :(

Answer 48

Here b=(1/4).

how did you obtain 2pi/3 earlier? Use the same approach. Don't guess.

Answer 49

Review our discussion all you want, but please don't guess.

Answer 50

ok ill try my best.

Answer 51

Believe me, you'll need to know this stuff where it pertains to trig functions!

Answer 52

If b is the coefficient of x in y=sin bx, then the period of y=sin bx is 2pi/b.
You MUST know this fact.

So, what is the period of y=sin (1/4)x?

Answer 53

I was given that, "The period of the sine function (of the form y=sin x) is 2pi." and I knew that since y=sin x is 2pi all I do is insert the 3 with the 2pi.

Answer 54

what do you mean by "insert the 3?" mystery meat. ;)

Answer 55

We all have a lot of holes in our bodies and have to be clear in specifying which one we mean for which purpose.

Answer 56

lol so the equation you gave previously was y=sin 3x, and I knew since y=sinx is 2pi I just do 3*2pi

Answer 57

So, Mark, what are you going to be doing with that 3?

Answer 58

oh divide

Answer 59

does your response match up with 2pi/b?

Answer 60

Let me put you on the spot. What's the formula 2p/b for? and where does 'b' come from?

Answer 61

sh im not so sure lol.

Answer 62

*ah

Answer 63

I gave you y=sin bx. b is the coefficient of the variable x.

The period of the sine function is 2pi. That's for y=sin 1x. b=1 here.
The period of the sine function y=sin bx is 2pi/b. Steal "b" from the function and divide that "b" into 2pi to obtain the period of y=sin bx

Answer 64

What is the period of y=3 sin (1/7)(x) ?

Answer 65

Hint: b is (1/7) here.

Answer 66

ah im confused, may you type it up please I just have trouble understanding. :(

Sorry for giving such a hard time.

Answer 67

Review: the period of y = sin bx is 2pi/b.

if b=(1/7), then the period of sin (1/7)(x) is \[\frac{ 2 \pi }{ \frac{ 1 }{ 7 } }=?\]

Answer 68

What's the rule for dividing something by a fraction?

Answer 69

is it 44.2?

Answer 70

I gotta divide fraction inside of fraction first.

Answer 71

I'd prefer you stick with symbols: (7/1)(2 pi) = 14 pi. Yes, 14 pi is approx. 44.2

Answer 72

Actually you gotta invert the fraction in the denominator and then mult.

Answer 73

oooh

Answer 74

so 2(7)=14(3.14)=43.96

Answer 75

So, the answer is merely 14 pi.

Back to the original question.

If y = f(x), then its graph is HORIZ. COMPRESSED to represent the graph of y=f(cx), where c is a positive number greater than 1.

Answer 76

1/c

Answer 77

Given y=f(x), the graph of y=f(4x) is horiz. compressed by a factor of 1/4 as compared to the graph of y=f(x).

Answer 78

Right you are.

Answer 79

haha finally!

Answer 80

Gotta get off the 'net (unless you have just one more question that is short).

Answer 81

no I have no more questions for now. I used notes to take the question. I use to cheat off the internet and thats why I don't understand much. I passed my other classes with cheating, but it brought me to this.

Answer 82

So I am just trying to understand much of what I did not learn before. :)

Answer 83

Raise me tomorrow if you have any pressing questions. Learning takes time, but it's generally very well worth that time.

Answer 84

Yea! You are right it takes time, and it is worth it because then you understand the concept without trying to cheat. I really appreciate your help! I sure will ask you if I have more questions. You are a very good helper. :)

Answer 85

Spasibo balshoye! :)

Answer 86

MANY THANKS, MARK

SPASIBO!

Answer 87

LOL! Alright ttyl brotha! :)

Answer 88

:)