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anonymous
 one year ago
Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term.
3x5 + 9x4 + 5x3 + 3
anonymous
 one year ago
Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. 3x5 + 9x4 + 5x3 + 3

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jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2So, have you been able to make sense of the question? Do you know what they are asking for? :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2Alright, so I'm guessing you don't know what "end behavior" is talking about?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2OK, great! It's always helpful to know where we are starting from. We can always build up our knowledge, but it's best to start on common ground. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay tell me what to do

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2Before we dive into "end behavior," let me finish the "interrogation" :) and ask if you could identify the leading term? Not trying to embarrass you or anything, just want to make sure I'm using language we both understand.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no, i havent studied any of this.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2OK, very good. Thanks for the heads up. Let's start by reviewing what a "term" is. :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2In math, we have two basic operations: addition and multiplication (let's ignore subtraction and division for now, because those are basically just opposites).

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2Usually, in algebra class we like (or not) to study polynomials: They usually look something like this: 2x^2 + 4x + 5 or this 5x^7 + 32x^4 + 3x + 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0in my case 3x5 + 9x4 + 5x3 + 3

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2That's right! Notice that our friends addition and multiplication are the "starring actors" here. We have multiplying numbers like the 2 in 2x^2 or the 4 in 4x. Or in our case the 3 in 3x^5 but we also have addition, like the 2x^2 + 4x or the 4x + 5. Or again, the 3x^5 + 9x^4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So is that our leading term ?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2Almost there. Wait for the punch line. :) When we multiply numbers, they "feel" closer. Even visually the 3 seems closer to the x^5 than the + sign. 3x^5 + 9x^4.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2A "term" is just the piece that is separated by a + sign. So, in our example, we have 4 terms: 3x^5, 9x^4, 5x^3, 3

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2We like to arrange our terms from "highest power of x" to lowest power. So in our example, 3x^5 is our leading term. That's the first part of your question.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2OK, now for that "end behavior" conversation. Have you had to graph anything in class yet?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no, well not in a long time. I'm not to good at math

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2That's fine, it's a rare person who is good at math automatically. It takes a lot of practice (let me tell you). :P Let's have a quick review of graphing, because that is where this "end behavior" stuff really comes to life.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2OK, so let's start with a very simple graph. The graph of 2x.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2If I wanted to make this polynomial into a picture, what could I do? It's not very obvious... but one way I could start to understand what 2x means is to plug in some numbers for x and see what the equation does to it.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2For example, when x = 0, 2x = 2(0) = 0 x = 1, 2x = 2(1) = 2 x = 2, 2x = 2(2) = 4 and so on. Does that make sense so far?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2Great, now for the picture part. We set up two number lines, one horizontal that we put our x on, and one vertical that we put our 2x on (most people call this the yaxis, but that's because they will say that y = 2x, it's an extra step, but we can skip over that for now.)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2Now, I will record the information that I just found above in picture formdw:1439358865094:dw

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2See how the dots match our information? The first dot is at x = 0, 2x = 0. The second dot is at x = 1, 2x = 2. And the third dot is at x = 2, 2x = 4.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2It's at little like the game Battleship, if you've ever played that. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmm i dont quite understand that graph :/

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2No worries, let me redraw it. It's not an obvious process. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh wait nvm, sorry my eyes are getting blurry lol

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2You got it? A good way to read it is to first look horizontally. For example find x = 1. Then with your eyes look up vertically until you see a dot. Then look to the left and you will see the value for 2x, in this case 2. :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2OK, so if you can imagine we kept doing this, plugging in numbers and so forth, we would eventually get something like this dw:1439359121271:dw

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2All of the dots we plot would sit on that line. It turns out that 2x does in fact make the picture of a line.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2Alright, then! What I am going to do now is to skip over a lot of actual graphing and just be "the expert" and tell you what many different graphs look like. This will help us understand what something like x^5 would look like if we graphed it. Prepare for an "art gallery" :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait, is the end behavior up and down, because the leading trm is negative and an odd nu,ber ?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2Aha! You seem to know the trick! :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0haha okay. So thats how I would explain my answer then ?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2In fact, you will get a picture like this for 3x^5:dw:1439359428939:dw

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2Yes, the leading coefficient (the highest power) always controls the end behavior. Your explanation was perfect! Congrats!

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2For future problems, I'd recommend checking your answer with this graphing tool: https://www.desmos.com/calculator just type in an equation and you can see the computer plot it for you. :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2It's a great way to see the meaning behind all the symbols.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, well thankyou for taking the time to explain it to me. :D Have a good night !

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.2Your welcome! Good night.
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