# Thread: Analyze and graph the polynomial function?

1. ## Analyze and graph the polynomial function?

I have a bunch of this to do and if I could get an example to go by, that would be awesome. Thanks to anyone who takes a look at it.

Analyze and graph the polynomial function: f(x)= 3x+3/2x+4 by filling in the following information.

1. Find Domain?

2. x-intercept(s)?

3. y-intercept(s)?

4. vertical asymptotes?

5. horizontal or oblique? (Determine if the graph intersects either of these asymptotes. If f(x) does intersect, find the point of intersection. If f(x) does not intersect, state that there is not an intersection point.)

6. Test for symmetry: Identify any symmetry f(x) has.

2. ## Re: Analyze and graph the polynomial function?

Originally Posted by wevie
Analyze and graph the polynomial function: f(x)= 3x+3/2x+4 by filling in the following information.
Is that supposed to be $f(x) = 3x + \frac32x + 4,$ as it's written, or is it $3x+\frac3{2x} + 4$ or $\frac{3x+3}{2x+4}?$ The second two are not polynomials, but the first one looks strange to me, as I would expect the two $x$ terms to have been combined.

3. ## Re: Analyze and graph the polynomial function?

Originally Posted by Reckoner
Is that supposed to be $f(x) = 3x + \frac32x + 4,$ as it's written, or is it $3x+\frac3{2x} + 4$ or $\frac{3x+3}{2x+4}?$ The second two are not polynomials, but the first one looks strange to me, as I would expect the two $x$ terms to have been combined.
$\frac{3x+3}{2x+4}$

It's this one. I will have to learn the tags if I hang around here very much.

4. ## Re: Analyze and graph the polynomial function?

Then the very first thing you need to learn is that this is NOT a polynomial. Now, do you know the definitions of such things as "domain", "x-intercept", "y-intercept", etc.? If not you can't possibly hope to do the problem until you look them up- probably in your text book.

5. ## Re: Analyze and graph the polynomial function?

Originally Posted by HallsofIvy
Then the very first thing you need to learn is that this is NOT a polynomial. Now, do you know the definitions of such things as "domain", "x-intercept", "y-intercept", etc.? If not you can't possibly hope to do the problem until you look them up- probably in your text book.

I now realize that that it is not a polynomial function. The reason I called it that in the first place is because that is exactly what the assignment says that the instructor gave us.

"Analyze and graph the polynomial function f(x) = $\frac{3x+3}{2x+4}$ by filling in the following information:"

Here is my story. I started back to college recently and when I took the assessment test to get into school, I scored pretty good in everything and didn't want to take anything that I did not have to, but I have quickly figured out that I could have most certainly used one or two lower level math classes for a refresher since I have opened a math book in something like 15 years. So now I find myself in pre-cal algebra. Up to this point, I have been doing OK but now I am seeing things that I have never seen or have not seen in a long time so I am a bit over my head. This is also a summer class in which we are covering 16 weeks of material in 8 weeks.

On top of that, the instructor is not up to the standard I would have hoped for. She spends the first 30 minutes of class hooking up her computer and digital pen or whatever it's called. Then she spends another 20 minutes or so talking about anything other then math. After that, she touches on this and that and when I get home and start working on the homework, I find there are things we never talked about in class.

But to answer your question, I do know what domain, range, intercepts, etc are. I was only trying to get a little help or maybe an explanation of how it is done. I am not trying to get someone to do all my work for me or anything. I have been a long time user of forums of different types and this looked like a good math forum.

When looking at this further, I have decided

domain is (-infinity,0) U (0,infinity)
x-intercept is (-1,0)
y-intercept is (0,3/4)
Vertical asymptote of -2
There is a horizontal asymptote of 3/2
There appears to be no symmetry

Maybe someone could have a look at my answers to see if they are right and if they are not, would someone mine explaining to me what I did wrong? Thanks

6. ## Re: Analyze and graph the polynomial function?

Taking an accelerated summer course after a 15-year gap is probably not the best idea.

Originally Posted by wevie
domain is $(-\infty, 0)\cup(0,\infty)$
How did you get this? Why are you excluding zero from the domain?

Originally Posted by wevie
x-intercept is $(-1,0)$
y-intercept is $\textstyle\left(0,\frac34\right)$
Right.

Originally Posted by wevie
Vertical asymptote of -2
There is a horizontal asymptote of 3/2
Your asymptotes should be lines. So your answers should be equations of lines: $x = -2$ is the vertical asymptote and $y = \frac32$ is the horizontal asymptote.

7. ## Re: Analyze and graph the polynomial function?

Originally Posted by wevie
I now realize that that it is not a polynomial function. The reason I called it that in the first place is because that is exactly what the assignment says that the instructor gave us.

"Analyze and graph the polynomial function f(x) = $\frac{3x+3}{2x+4}$ by filling in the following information:"

Your instructor's incorrect. That is definitely not a polynomial function.

Also, your answers seem correct, except that the domain is not $(-\infty, 0) \cup (0, \infty)$. The domain is any real number except those which make the function undefined or indeterminate. Here, if x = -2, the function is not defined. Therefore the domain is $(-\infty, -2) \cup (-2, \infty)$.

8. ## Re: Analyze and graph the polynomial function?

The function is $f(x)= \frac{3x+ 3}{2x+4}$. When x= 0, $\frac{3}{4}$. There is nothing wrong with that! You may be thinking of the fact that 1/x does not have 0 in its domain. That is because 0 makes the denominator and you cannot divide by 0. Here, the denominator is 2x+ 4. What value of x makes that 0?

9. ## Re: Analyze and graph the polynomial function?

Originally Posted by HallsofIvy
The function is $f(x)= \frac{3x+ 3}{2x+4}$. When x= 0, $\frac{3}{4}$. There is nothing wrong with that! You may be thinking of the fact that 1/x does not have 0 in its domain. That is because 0 makes the denominator and you cannot divide by 0. Here, the denominator is 2x+ 4. What value of x makes that 0?
Yeah this is what I was thinking. That and the fact that when I looked at the graph, it seemed to steer away from 0. So for the domain, I should replace 0 with -2 then or 2? richard1234 shows it as 2.

It would be -2 right? (2*-4)+4=0

10. ## Re: Analyze and graph the polynomial function?

Yeah, -2, sorry about that. 2x+4 = 0 --> x = -2.