Supplement #3

I know that no one will be able to answer this tonight, but I still want to know how to do this.
How do you solve 3^(x^2)/3^(3x)=1/9 in Chapter 3 Supplement #3?

Ch 4 Supplement

I know this is a little late, but if anyone knows how to do the difference quotient for g(x)=f(x)+c, could you possibly come talk to me about it.

Response to Elena

Actually, symmetry across the origin is an odd function and aross the y-axis is an even function. Symmetry across the x-axis would be a zero function because there are two y colutions for every x value, and that is illegal.

function question

So if the function is even it is symmetrical over th y-axis? And if it is odd it has symmetry over the x-axis? And if it is neither it has symmetry over the origin? Or am I wrong? Cuz when I went to tutoring afetr school they told me something different.

instantaneous rate of change (value of h)

The intstantaneous rate of change is taken when ha is infinitely small. Two questions about this:

1. How do you write this on paper?

2. Is there any way to make your calculator display calculate the average rate of change?

Group Work Due Date?

When is the group work functions worksheet due? And who was in my group?

question

I have a question as to classes in the math department... is it required to had taken AP Cal to take AP Stats, and if you are going to a medical feild do u think it is necessary to take Stats in college? melissa

logarithms

just out of curiousity, when do we use logarithms in real life?

An asymptote is...

An asymptote is a curve that gets arbitrarily close to another curve or line, but never actually touches. Having x "approach" 3 is the same thing as having a vertical asymptote at 3. The graph 1/x will give you a vertical asymptote at x=0 and a horizontal asymptote at y=0.

Group Work on Functions

I am confused on problem #7 on the "Group Work on Functions" sheet. Someone told me the function Df(x)=x^2+xh+h has already simplified, and we just need to substitute in numbers, we don't need to use (f(b)-f(a))/b-a to find the ARC (and the IRC). Is that correct? and how to do this problem?

Graphing Inverse Functions on TI89

On our calculators it's not possible to computer the inverse of an inverse in any reasonably simple way, however you actually can draw it on top of another graph if you wanted to see what it looked like. So go to the Y= screen and enter in x^2 for y1, then go to Graph, and hit 2nd+F6>3 (DrawInv). This will take you to the home screen and after the DrawInv part type in y1(x). It should look like "DrawInv y1(x)" and you can then hit enter. It will then take you to the graph screen again, and show you the original graph and its inverse. Note that you cannot actually do any math with this inverse graph, and it serves merely as a visual reference.

IRC

I'm still somewhat confused about finding the instantaneous rate of change, especially when looking at a graph. I know if you are given the function yous use the difference quotient and a small h. However, when you have a graph is it more than an estimate? By this I mean do you do more than just find a close coordinate and use that value to find the slope?

2 Questions

1. my first question is about questions 7 and 8 on the pretest: how do you justify the domains algebraically?

2. what is an asymptote (like in question 14 on the pretest)?

thanks

Clarification for Practice Test, #3

Even though this came up during the review session on Monday, I still felt it would be helpful:

For number 3, it's asking to find the graph of f(x) after its transformation. You scale the graph by a factor of 1/2 and not 2 because you can set the function to equal y. (it works because for any x you plug into the function, you will get a y out.)

1/2(f(x/3))=y
2*1/2(f(x/3))=2*y
f(x/3)=2*y

now you can see that the original graph is being scaled by 1/2 because you do the inverse operation when graphing.

Too simple?

Hi this may be obvious but number 48 on the Ch. 3 review says if -5 is less than or equal to a is less than b is less or equal to than 6. Then they ask is a less than b. This is true right? It seemed too simple so I apologize for this silly question.

Average Rate of Change Question...help

What is the primary difference between ARC and IRC?

Is ARC the slope of the secant line between two poits and IRC the difference quotient? I'm confused.

Answer to Sarah's Question

The Difference Quotient is:

(f(x+h)-f(x))/h

for the difference quotient, is it f(x+h)-f(x)/ h or f(x)-f(x+h)/h

i meant to ask earlier but blogger i was having issues with blogger

Thanks for the help everybody

thanks battlejoe i understand how now. I also want to say sorry to the people that i argued with in the tutoring section today and thanks for the clarification everybody. i think i am going to do well on this test because of you guys. another question though, on 23 in the review chapter 3, i forgot how you plug in the x and y value. i tried my way and it turned out like a straight line. can someone help me? thanks a whole lot!!! melissa

Response to Melissa's question

The calculator will show you the solution to an inverse equation if you plug in the old equation and take it to the power of -1 like this
(3x+5)^-1 = 1/(3x+5).

This will solve for any equation.

number 49

For 3.7 number 49, how would you approach the problem?

Pre-Test Problem 11

I am really stuck on this problem on the Pre Test, It is one of the only ones that I have left to complete, and if any one has some tips about solving these forms of function problems I would appreciate it. I am having a little trouble grasping these problems with functions of times and distance, so any suggestions would be nice.

Round-Tip Theorums

October 22, 2006. I understand the inverse functions but if I am putting it in the calculator how do I do it? and I sort of understand the theorum but could someone clarify for me? thanks. melissa

Round-Trip Theorum

How are you supposed to use the Round-Trip Theorum in problem 3.7.25?

TI-89: Converting Temperatures

This is a response to Manny's question that he posted about a week ago, but may be useful to others. When converting temps, you can't just use the standard notation I discussed a couple weeks ago, because the calculator thinks the degrees sign is referring to an angle measure. You have to use the tmpCnv() function found in the catalog under T. The first argument is the "from" temp with value and units, the second argument is the "to" unit. Here's an example:
tmpCnv(32_°F,_°C)
= 0_°C

--Steve

For Those Who Need Help With Inverse Functions

Here are two websites that I found to be extremely helpful. Both give indepth information and insights on inverse functions.

http://www.purplemath.com/modules/invrsfcn.htm
For this website, scroll down to the bottom to navigate through the pages whcih might be of help, depending on what your questions are.

http://www.uncwil.edu/courses/mat111hb/functions/inverse/inverse.html

Inverse Functions and graphing them HELP!!

I wasnt here friday so Im kind of lost on the inverse function homework. Im trying to figure it out but I dont have my book with me so can someone briefly summarize how to find inverses of functions, please?? Thanks so much!

finding inverse functions

I'm having trouble finding inverse functions. Does anyone have any general tips? Or more specfically problems like 13 and 17 in the homework from section 3.7.

pretest due date

what day was the pretest due again in order to receive the eight points?

Response to Sarah's Question

You would do:

d(10) - d(0)
___________

10

this would give you an average speed of 14 feet/second

The reason you would do this is because the time between 0 and 5 needs to be included.

3.6.1a

when you find the average speed from 0 seconds to 10 seconds would you do

d(10)-d(0) and get 140

or

d(10)-d(5) and get 120

im not completely sure

answer to Brian's question

When you scale the y side of the equation, you use the inverse of the scale of y on that same side, and to flip it to the otherside, we obviously divide. It is just important to remember that the inverse function is always what we want to do.

Answering Yuchen's question

Yuchen,

It's debatable whether or not it should be inclusive but maybe your value of 3.5 was too far off the solution he was looking for.

Quiz # 1 and 2

Does anyone understand why you would put the multiplication for the translation on the side of the equation opposite the f(x) even if it is a problem when y is scaled?

About #25

ff= X^3*X^3=X^6. f(f(x))= ((x^3) )^3=X^9

-Fishface

Quiz 1-3

On the quiz for number 4. The correct answer is scaled first then translated left, but if you scale by 1/4 first then replace the x with x + 8 wouldnt you get 4(x+8) + 1 instead of 4x + 9? What am I missing?

Question for the TI-89

Does anyone know how to convert Fahrenheit to Celsius using the units and 2nd mode key? I keep getting inconsisent units.

Confusion #25

since we did the TMP #16-20 last time we dont need to do it right? and could anyone explain to me how to do #25 in the homework? I dont understand. Thanks Melissa

Number 33

For number 33 from section 3.5, does anyone know how to go about finding the rule of the function f(x)? How can we fill in the chart based on just one set of values?

Mr. K's Period 4 Precalc Blog

for number 21(4*5+1) on the hw 3.5 wut does it mean by the rule of the function?

Question on the Quiz

I had "quiz1-3".
For question #9 (the last question), "find all intervals on which f is concave up". I did -6<=x<=3.5, but x<=3.5 was wrong, I don't know why. What should be the right answer? Can someone help me?

Statistics Function on TI-89

A student currently taking physics asked me on AIM the other day how one would calculate the standard deviation of a set of numbers on their calculator. The function for standard deviation on a TI-89 is stdDev(), unlike excel which uses stdev(). You just have to input a set of numbers that's comma delimited and enclosed in braces. The function stdDev() among others is located in the statistics submenu of math (2nd+5), and braces can be entered with 2nd+( or 2nd+).



So if we have stdDev({0.9,1.0,1.1}), the calculator will return a value of .1. This is a lot easier than using the formula which is definately a nightmare. Oh sigma. Also located in the statistics submenu is the mean() function for calculating average and the median() function for finding the number in a set that separates the higher half from the lower half of numbers. Both functions work the same way as stdDev(), and are comma delimited.

an easy time saver on the 89

If you press [2nd>Home] in any application on the calculator, the menus at the top will be replaced with a set of handy menus with nice shortcuts for various things. Some example options on this special menu configuration:

• In the second menu, there's an option to insert "Define f(x) = " and then you can put in your funtion.
• In the third menu, there's an option to insert "solve( and , {x,y})" and you can just insert your two equations before and after the " and ".
• In the fourth menu, there are various common units which can be inserted to use with unit conversion (which I explained last time.)

Laziness prevails!

--Steve

What is (4n+1) on homework?

On homework 15 it says that you should do 3.5: 1-29(4n+1). Did he mention what this means? Anyone know?

Setting a Function on TI-89

When you're on the home screen, press f4, and then hit enter. Define will appear on the screen, then press alpha, f, (x)= whatever you want
press enter and it will respond with done, now when you type f(whatever) it will pop out an answer.

Unit Circle Stuff

So how do I go about finding a point on the unit circle with a certain x value.

P.S. I was the 1000th hit on the mr.karafiol's homepage!

tip about finding a viewing window

here's something i learned about graphing:

i know some people still do this, and its wrong! when you trying to find a good window, DO NOT USE ZOOM FIT! i was getting help from mr k one day during lunch and he asked me what i saw when i graphed one of the equations, it looked like an asymptote and i said it was, but mr k made it extremely clear that it wasnt. so lesson learned: zoom fit = dumb even though you are trying to find a good window b/c it makes your graph appear as something its not.

i'd suggest making some good estimates by looking at the equation being graphed or do some guessing and checking unless there's an easier way about it which id be glad to hear.

-sarah i

functions with calculators

when i was putting functions into the Y=...it would not accept the x greater than or less than at the same time. can anyone tell me how to get it at the same time? thanks.

asymptotes

what exactly is an asymptote of a graph?

multiple parametric equations

Can anyone explain how it works when you graph multiple equationsin parametric mode?

Example:
3.3 #99

How Do I Set Functions on a TI-89?

How do I set a function of something on the calculator and let the calculator solve for x or any given variable in an expression, according to that function. We may have gone over this in class but for some reason I did not record it in my notes.

Calculator Help

This isn't a major issue but i was wondering if anyone knows how to find the cubed root of a number on the TI-89. I know that you can find the number using the inverse of the root you're looking for (ie. cubed root of 8 = 8^1/3) but i was wondering if there's a way you can just type it into the calculator like with the TI-83. Again, not a crisis, I was just curious.

thanks

Problem

Does anyone understand how to do 3.4 #11?

Response to Brian's question

It would be shifted down, for example y+5=f(x-5) is equal to y=f(x-5)-5, so it will be shifted right 5 and down 5

Response to Transformation

In response to Brian's question, it would be shifted down. Working backwards, y=f(x) - 1 is equal to y+1=f(x) and the inverse of addition is subtraction, so it would be minus 1 on the y-axis, moving it down one.

For graph transformations of functions, I know that if there is subtraction inside the function it is shifted right, but if there is subtraction outside the function on the same side of the equation is it shifted up or down?

parametric graphs and questions concerning scaling

1. For Carrie, did you subtitue t for y and did you also state in y1 that y=t. This should work.
2. The book is kind of confusing me with the scaling of graphs. I thought when you scale a graph by a factor of a, the equation needs to have input the value of 1/a, or whatever the inverse of the scale may be. Can someone clarify this?

Unit Conversion

This may be useful in your science class:
The TI-89 has built in unit conversion! First, type in the value of the measurement you're converting from. Next, hit 2nd>3 to get to the units menu, find your unit (of the measurement you're converting from), and hit enter. Next, hit 2nd>MODE to get a little triangle arrow thing. Finally, go back into the units menu, and enter the unit that you're converting to. Hit enter and the conversion will be done for you! If you can remember what each unit is, you can just type it, rather than finding it in the units menu.
Example:
1_in>_cm
= 2.54_cm

--Steve

Response to Casey's question

I found 7 by using a similar viewing mindow as you but when it looked crowded on the graph, I zoomed in. It is surprising how little you see when you are zoomed out so far. The way the calculator works is it only shows you what it can fit. This means that the farther you zoom out the more your graph is going to look like a line. It can only show you so much because the pixels are only so small.

3.3.99

For this problem, I graphed xt1=(t^2-1)*(t^2-4)*(t+5)+t+3 and yt1=(t^2-1)*(t^2-4)*(t^3+4)+t-1, and no matter how I adjusted my viewing window, the curve only appeared to cross itself in 3 places... but the book said 7. This was my viewing window:
tmin: -2.5
tmax: 2.5
tstep: 1
xmin: -10
xmax: 50
xscl:1
ymin:-20
ymax:20
yscl:1
Did anyone find a viewing window that showed the curve crossing itself more than 3 times?

3.3 # 85+87

I thought that you were supposed to switch the mode from function to parametric and then graph the equations that way for numbers 85 and 87 in section 3.3. I tried this but then i couldn't find the graphs. Any ideas?

edline

does anyone know what Ch. 1 GW is on edline by chance?

3.2 # 70

for 70, i understand what the problem is asking for, but i have absolutely no clue as to how to set up the rule for it. How would i go about this?

Question 83

Question 83 is a puzzler, but once you think about it the right way it can be easy. Instead of thinking about the problem as the function you need. Think about it as only the graph. So instead of trying to decipher a function that would fit the guidelines, just draw the picture. Start with your axes, write in your scale ( have them reflect your Domaain and Range), and draw a picture that mathes the rules. Make sure that it's a function (that there are no two y's for a single x)

Sincerely,
Fishface

trouble with graphs

hi guys can someone please explain to me how to read the graph on homework...3.3#83, or something like that. after i look at the answer i sort of understood it but can someone make it a little clearer. thanks melissa

[re]:question 32 c

when the calculator simplifies (1/r-1/x)/(r-x), it puts the (1/r-1/x) over a common denominator then multiplies the result by 1/(r-x). It factors out negative 1 from (r-x) to -1(x-r), in the denominator and that cancels the x-r in the numerator, (from finding common denominator first. Finally, you are left with 1/rx times -1, which equals -1/rx.

(Possibly Useless) Calculator Tips

Sometimes you hit graph and you realize you've made a mistake and need to fix the equation, but oh no, the calculator won't let you go back and fix it until its finished with the graph its working on. But that could take another second! Time is precious when you're taking a test. You need to tell that calculator to STOP! And to to that, hit the "ON" key while its making a graph. It will stop making the graph and now you can go back and fix the equation and try graphing again.

Q: Why can't I enter numbers in my favorite form: binary and/or hexadecimal? ...you may ask. A: Well, you can! To enter a binary number, it must be prefixed with 0b (that is, zero b). For example, if you type in 0b10 and hit enter, it will tell you its 2, which is the decimal equivalent. Now hold on, you can do hexadecimal too! You just need to type in 0h (zero h) before the hex number. For example, 0hFF will give you 255.

Q: Oh I miss the entry style of the TI-83 so much, where you can overwrite a character when you have the flashing box over it, what can I do?
A: Well, to go back to the input style of the TI-83, hit 2nd and then backspace. This will toggle between overwriting, and inserting in between, for when you type stuff in.

--Steve

Isn't PI rational?

PI is equal to the the circumference over the diameter of any given circle. Now, circumference and diameter are both measurements. Aren't measurements rational? Can you have a measurement of infinite precision? Shouldn't any measurement terminate somewhere? Well, if that's the case, it would make PI the ratio of two rational numbers, making itself rational. Therefore PI is rational. Any thoughts?

--Steve

Don't Fall Behind!

I spent a few hours this weekend catching up on a couple homework assignments I've neglected earlier this week and it sucks to have it all pile up. And just to illustrate what I mean, I'll have you know this is my first blog entry. (Though I initially had problems trying post because apparently I have two separate accounts on blogger, but I guess that's beside the point.) But anyway, its best to get things done right away. I have a tendency to think of math homework as less important than other stuff mainly because I generally understand the material just from class. I'm not sure where I'm going with all of this, but I'll just urge you to get you're math homework done on time.

--Steve

Special graphs

I dont understand graphing functions. How do you read a function graph and name its domain and range, if for part of the graph x is greater than 2 and for another part x is less than or equal to 2. Wouldnt that make the domain all real numbers? Im not sure if I'm describing function graphs or peicewise graphs or what, so can someone also tell me what I'm describing? The graph is broken up and at some ends there is an open circle and at other ends there is a closed circle. Help.

TMP Sheet

Can someone please explain to me exactly how you're supposed to do the chart on the Two More Points sheet that's due tomorrow? I filled it out but im having trouble understanding what you're supposed to infer/gain from doing what it says.

TMP Sheet

Can someone please explain to me exactly how you're supposed to do the chart on the Two More Points sheet that's due tomorrow? I filled it out but im having trouble understanding what you're supposed to infer/gain from doing what it says.

TMP Sheet

Can someone please explain to me exactly how you're supposed to do the chart on the Two More Points sheet that's due tomorrow? I filled it out but im having trouble understanding what you're supposed to infer/gain from doing what it says.

3.2 #44

So i graphed each equation but im still confused on wut to do from there....for example how do i set the graph to find y when x equals -2.5

Troubles with the calculator and graphs

Can somebody explain to me how to read sign graphs, i forgot how...in the questions of 3.2, #41 and 42?And i have a question as to how to get the x and y coordinates on the calculator seperately. Thanks very much, everybody!
confused melissa

response to 73 (posted below)

Since the rectangle has an area of 6000 square feet and area = length * width, you can make the variable for the length of the rectangle x and the width 6000/x. The cost for the first three sides would therefore be 3.75(6000/x + 6000/x + x) and the cost for the fourth side would be 2x, making the function for the total cost f(x)= 3.75(12000/x +x) + 2x. That simplifies to the answer in the back of the book.

3.2.73 and TMP#9

I'm having trouble setting up number 73 in section 3.2. If someone could get me started I would appreciate it. Also, for number nine on the TMP sheet I tried starting by finding the slope of the graph with the given points but its quadratic so not sure that this helps and I don't know how to continue. Any ideas?

Calculator Phun

This is a neat trick for switching between applications or anything else that takes more than three buttons to switch between. If you push 2nd APPS then the calc will take you to the last thing you were looking at. If you push it again it will take you back to what you were at when you first pressed it. But dont take my word for it. Try it for yourself!