Question

How do I determine the end behavior of a graph?

Answer 1

You must use limits.

Answer 2

What's "limits"?

Answer 3

http://en.wikipedia.org/wiki/Limit_of_a_function

Answer 4

I assume you haven't done calculus yet?

Answer 5

end behaviour of a graph or a function?

Answer 6

A graph, they didn't give me the function

Answer 7

A graph is a function.

Answer 8

Isn't a function f(x)......?

Answer 9

Someone please help me, I ONLY have the graph to go by.

Answer 10

Can you post the graph as an attachment?

Answer 11

I can't sorry, but I CAN tell you this...............

The function is an odd degree
The leading coefficient is negative
It has one real root
The real root is -1.5
The minimum degree is 3 (two bumps)

Answer 12

The "end behaviour" to the right is negative infinity, the "end behaviour" to the left is positive infinity.

Answer 13

How can I tell?

Answer 14

The leading term always dominates the rest of the terms as x approaches positive or negative infinity.

Answer 15

??????????????????????????

Answer 16

\[\lim_{x \to +\infty}-x^{2n + 1} = -\infty \]\[\lim_{x \to -\infty}-x^{2n + 1} = \infty \]Where n is a positive integer.

Answer 17

Look at the leading term and think about what happens when x is very large

Answer 18

Thanks anyway, I'll just guess on that one I guess for my test out Wednesday. I kind of get it, thanks

Answer 19

What's the leading term? And what do you mean by left and right?

Answer 20

These are graphs of polynomials I'm assuming and you want the end behaviour of the graph.

Answer 21

By end behaviour they are talking about what happens as you go further and further to the right of the graph or further and further to the left of the graph.

Answer 22

By leading term I mean the term of the polynomial raised to the highest power.

Answer 23

You said the "function is of an odd degree" this means the leading term is raised to an odd power

Answer 24

One more question....... I promise! I'm finally getting it now. On my packet, the possible answers look like this.......

Answer 25

\[f(x)\rightarrow-\infty, as x \rightarrow+\infty and f(x)\rightarrow+\infty, as x \rightarrow-\infty\]

Answer 26

The other three options have different +- combinations

Answer 27

How do I know which one to choose?

Answer 28

The "end behaviour" depends only on the degree of the polynomial and whether the coefficient of the leading term is negative or positive. I will make a table in a moment

Answer 29

So what's the degree?

Answer 30

The leading term?

Answer 31

\[Wait, so there's f(x)\rightarrow and x \rightarrow\]

Answer 32

Which one of those two is the chart for? the x? If it is, then what about f(x)?

Answer 33

Polynomial function:
\[f(x)=a_0x^n + a_1x^{n-1} + ... + a_n\]
\[\text{The leading term is the term raised to the highest power.}\]\[\text{So look at if $a_0$ is positive or negative, and if n is even or odd.}\]
\begin{array}{c|c|c|c}
\text{Degree (Even/Odd)} & \text{Leading term ($\pm$)} & x \to -\infty & x \to +\infty \\
\hline
Even & + & f(x) \to +\infty & f(x) \to +\infty \\
\hline
Even & - & f(x) \to -\infty & f(x) \to -\infty \\
\hline
Odd & + &f(x) \to -\infty & f(x) \to +\infty \\
\hline
Odd & - & f(x) \to +\infty & f(x) \to -\infty \\
\end{array}

Answer 34

There's f(x) AND x so is the chart above for the x? If so, what about the signs for f(x)?

Answer 35

Hello?

Answer 36

The first line of the table would be:
\[\text{$f(x)\to+\infty$ as $x \to -\infty$}\]\[\text{$f(x)\to+\infty$ as $x \to +\infty$}\]
The second line of the table would be:
\[\text{$f(x)\to-\infty$ as $x \to -\infty$}\]\[\text{$f(x)\to-\infty$ as $x \to +\infty$}\]etc.

Answer 37

Do you see what I mean?

Answer 38

For the question you posted you would select the last line.

Answer 39

The polynomial is odd and the coefficient of the leading term is negative, so use the last line, etc.

Answer 40

No, one of the options that I posted with the arrows and infinity symbols to give you an idea of what the answers looked like, that was all one, not two

Answer 41

It is "all one"

Answer 42

You are looking at what happens as x goes to negative infinity AND what happens when x goes to positive infinity

Answer 43

The answer for your current question is:
\[\text{$f(x)\to+\infty$ as $x \to -\infty$}\]\[\text{$f(x)\to-\infty$ as $x \to +\infty$}\]

Answer 44

Yeah. it's all one options, there are three others like it. And what you just posted isn't an option for an answer.....

Answer 45

What are the options?

Answer 46

I'll give you each one and tell me if it's right or not.

Answer 47

\[f(x)\rightarrow-\infty, as x \rightarrow+\infty and f(x)\rightarrow+\infty, as x \rightarrow-\infty\]

Answer 48

That's ONE option

Answer 49

Do you not see how my answer above is the same as that option...

Answer 50

Is the chart that you gave me for the x or f(x)?

Answer 51

The order doesn't matter.
\[\text{$f(x)\to+\infty$ as $x \to -\infty$}\]\[\text{$f(x)\to-\infty$ as $x \to +\infty$}\]

Is the same answer as:
\[\text{$f(x)\to-\infty$ as $x \to +\infty$}\]\[\text{$f(x)\to+\infty$ as $x \to -\infty$}\]or
\[\text{$f(x)\to-\infty$ as $x \to +\infty$ AND $f(x)\to+\infty$ as $x \to -\infty$}\]

Answer 52

Oh, ok, I didn't know that. With the chart that you gave me, I got \[f(x)\rightarrow \infty as x \rightarrow-\infty\] so then would I just do the opposite of that result for the second part of my answer?

Answer 53

No look at the chart, there are two sections in each line

Answer 54

Or is it cut off in your browser?

Answer 55

OOOOHHHHH! Wow! Blonde moment! I can't thank you enough for your amazing help! But then it says write your answer in function notation?????

Answer 56

Sorry I don't know what they mean by that.

Answer 57

Thank you so much! I'll just guess on that one.