Graphing rational functions???

[iPwn]

So anyway we missed a few days because of snow in my math class and now the class is complete nonsense and I'm so far lost. Luckily, because of being behind, every test so far has been a take home test that I could just get help on and get an A.

Anyway so I'm not sitting around doodling for three hours tomorrow night I need to figure out how to learn what we did last week...He made no sense..

How do you graph rational functions??

He like made a # line below the graph with all these divisions and divided the graph up and did some crazy stuff with + and - signs to figure something out about how the lines should go or something...

Also something to do with asymptotes and such which I don't even understand. I copied everything down that he wrote but it's like jibberish.. I don't understand how you decide what each part of the graph should look like and where it should go...

Also theres stuff like "as x->1 (with a negative sign up top saying as x gets near 1 from the right) f(x) -> (negative infinity)...... I don't have a freaking clue and was wondering if anyone could put this in human terms....

If not sorry, but this stuff is like Japanese to me....I understood the whole way up to doing that fog and gof stuff and graphing quadratic functions but this stuff is insanely crazy.

 

[galactus]

Post a specific problem and we'll see what we can do. There are easy ways to find asymptotes.

 

[iPwn]

Okay...well g(x) = 3x / x+2

So I have written down that the vertical asymptote thinger is -2, I guess that is always what makes the denominator 0?

Then the horizontal says y=3.... Not a clue how he got that..

so then there is a # line that says negative infinity to -2, -2 to 0 and 0 to infinity..

then it has 3x then x+2 over top of eachother... 3x left of 02 is -, x+2 left of -2 is - so then it says positive..... and so on..

the graph is divided up with dotted lines at those points... -2, and 0 and a horizontal line at y=3....

then it says "as x goes to infinity, f(x) goes to 3...as x goes to -ifnitity, f(x) goes to 3, as x goes to -2 from the right, f(x) goes to infinity, and as x goes to 2, f(x) goes to negative infinity

and then he just threw two sketches of graphs on there out of the blue it seems to me...


I couldn't be more lost.

 

[stapel]

So anyway we missed a few days.... I need to figure out how to learn what we did last week....
How do you graph rational functions?
...Also something to do with asymptotes....

Since we cannot reasonably replicate the missing hours of classroom instruction within this environment, please consider studying some of the many lessons available online.

. . . . .Google results for "rational expressions domain"

. . . . .Google results for "graphing rational functions"

. . . . .Google results for "asymptotes"

Working with the lessons you find online, along with your textbook and the classnotes you've gotten from friends, you should be able to get caught up in just a few hours' study.

Once you've learned the basic terms and techniques, if you have difficulty with a specific exercise, please show all of your work and reasoning, and we'll be glad to help you past any sticking points.

Thank you.

Eliz.

 

[galactus]

You have your vertical OK.

Now, for the horizontal. There are 3 little rules you can use to make it easy.

If the power of the numerator is greater than the power of the denominator, then the graph has no asymptote.

If the power of the numerator is the same as the power of the denominator, then the line made up of the ratio of the leading coefficients is the asymptote.

If the power of the numerator is less than the power of the denominator, then the x-axis is the asymptote.

You are the second one. The powers are the same. All this means is you take the leading coefficients of the numerator and denominator and make a line from the ratio
\(\displaystyle \L\\y=\frac{a_{n}}{b_{k}}\).

\(\displaystyle \L\\\frac{\overbrace{3}^{\text{a_n}}x}{\underbrace{1}_{\text{b_k}}x+2}\)

Your leading coefficients are \(\displaystyle a_{n}=3\) and \(\displaystyle b_{k}=1\). Therefore, the line y=3/1=3 is the horizontal asymptote.

Another thing is, as x increases, f(x) approaches 3

Try x=1000 and you get 2.9940...

Try x=1000000 and you get 2.99999

Now, try the other side. As x approaches negative infinity, you will approach 3 also, only from the other side.

If you enter in -1000000, you get 3.000006...

See?.

You can see that from the graph.

See?. Close and closer to 3 the larger you get. As x approaches infinity, f(x) approaches 3.

Here's the graph so you can see:

Picture a horizontal line at y=3. You can see that's the asymptote.

Does this clear it up a little?.

 

[iPwn]

As far as the asymptotes, yes that clears it up...But what about the as x goes to infinity this does that and all that, and the # line thing?

I don't understand how you figure out what the thing is supposed to look like and what way it is supposed to go so you can sketch it...

btw Stapel, I didn't miss class, I was just totally lost in class....... I didn't feel like sticking around afterwards for help because I was so confused I just got angry and left...I hate this stuff with a passion.

I did google for this but none of the pages I found had anything to do with a # line and some of the pages just confused me more....if that's possible....

 

[galactus]

Sketch it?. Don't you have a graphing calculator?. Who sketches anymore?.

I amended my post explaining the infinity thing.

Hating something with a passion will only cause you heartache. Relax.

If you must graph by hand, just enter in various values in f(x) and plot them.

 

[iPwn]

Sketch it?. Don't you have a graphing calculator?. Who sketches anymore?.

I amended my post explaining the infinity thing.

Hating something with a passion will only cause you heartache. Relax.

If you must graph by hand, just enter in various values in f(x) and plot them.

We're not allowed to use calculators.... He's all like "After this class you'll know if your calculator is right"...


I understand whta your saying about that infinity crap, but he taught us to do it with a number line and I don't understand that...If he wants us to do it that way it would make sense to do it that way....

Especially for the ones that go through more than one section of the graph...Somehow using that numberline I guess tells you that it goes up in one section, down in the next section and then back up in the next section...But I don't understand that concept at all...

About graphing by hand...We are just supposed to sketch it with the information we know, not using a table of values...The book uses a table of values but we're not using calculators so basically he just wants the behavior of the graph to be accurate.


We're doing exponential and lograthimic functions tomorrow..... Do I need to know how to do this stuff to do that? If not I might as well not even bother because I'm never taking a math course again, and I assume he'll keep giving us take home tests (except for the final) since we are pressed for time.

 

[stapel]

...we missed a few days because of snow....

btw Stapel, I didn't miss class...I didn't feel like sticking around...I just got angry and left.

My apologies: When you said you'd "missed a few days because of snow", I'd mistakenly assumed that you'd missed class due to snow. I hadn't realized you'd just blown off class because the topic under discussion ticked you off. My bad. :roll:

none of the pages I found had anything to do with a # line

Since we cannot see the "jibberish[sic]" that you claim the instructor provided, nor what you mean by "a # line" ("a number line", for English speakers), there is little way for us to advise. Sorry.

If nothing online or in your book or from your instructor has helped at all, and you have no idea what has been going on for the last few weeks or months (as evidenced by the many take-home tests you say you've faked with online help), then I would strongly advise a serious talk with your academic advisor regarding more-appropriate course placement.

My best wishes to you.

Eliz.

 

[iPwn]

...we missed a few days because of snow....

btw Stapel, I didn't miss class...I didn't feel like sticking around...I just got angry and left.

My apologies: When you said you'd "missed a few days because of snow", I'd mistakenly assumed that you'd missed class due to snow. I hadn't realized you'd just blown off class because the topic under discussion ticked you off. My bad. :roll:

none of the pages I found had anything to do with a # line

Since we cannot see the "jibberish[sic]" that you claim the instructor provided, nor what you mean by "a # line" ("a number line", for English speakers), there is little way for us to advise. Sorry.

If nothing online or in your book or from your instructor has helped at all, and you have no idea what has been going on for the last few weeks or months (as evidenced by the many take-home tests you say you've faked with online help), then I would strongly advise a serious talk with your academic advisor regarding more-appropriate course placement.

My best wishes to you.

Eliz.

You misinterpreted everything I have said...

I have NEVER missed a class and have ALWAYS stayed the entire three hours...What I said was I didn't stay AFTER class last week for help because I was lost and angry... I figured I could figure it out on my own, which I can't...

I have not cheated on ANY of the take home tests, even the one I did today I did on my own with no help other than from my notes.... I know how to do everything but what we learned last week, and it's all really easy except for this stuff....

Dropping this and taking another course would be stupid, there are five weeks left in the semester and I have an A in the class as it is.... It is also is my last math class ever.

I haven't been lost at all until last week.


I am not "blowing the class off" I have been staring at my notes for the last three hours (after I finished the test) trying to figure last week out.... Then I came online and posted on GameSpot where no one could help me so I came here, where someone did help me a good deal.

You don't have to be all grumpy about it...If you don't want to offer help, just don't do it. Don't go and say I'm a crappy student. I am not, I simply hate math...so what, who doesn't?

Whatever...I'm going into class early tomorrow to see what he can do for me.

Thanks galactus.

 

[jwpaine]

I created this for myself a few days ago... feel free to print it and stick it in your 3-ring binder.

http://jpaine.net/math/rational.pdf

make a table of x and f(x) pick some points for x and substitute them into your rational function f(x)

plot them. if f(x) is undefined (divide by zero) then you have substituted a point that is beyond an asymptote.

Hope this helps.