struggling with weird graphs: y=x/x^2-9, y=x^2/x^2-16, ...

[Mitsukuni]

My math teacher had explained these graphs (or at least tried to) to me. It got to the point where he was explaining it for like the 10th time and I still didn't get it. So I did what a normal kid would do and just nodded and told him I got it even though I had no idea what's happening. So I'm turning to the internet to help me with this. Can anyone explain the methods to graph these equations? (or just show me pictures of working out, that would help me heaps)

y=x/(x^2-9)
y=(x^2)/(x^2-16)
y=(x^2)/(x-2)
y=(4-x^2)/(4+x^2)
etc.

All I got so far is that limits and asymptotes are things that you need to know to graph these (yeah, that's practically nothing).

---

MORE INFO: This is my working out for the first question. I also included the parts that I know that I need but don't actually know how to get.

y=x/(x^2-9)
Vertical asymptote:
x^2-9=0
x=3, -3

Horizontal asymptote:
???

Intercepts:
When x=0,
y=0/(0^2-9)= 0
When y=0,
0=x/(x^2-9)= 0
Therefore, eqn passes through the point (0,0)

Limits [knowledge of limits is practically nil]
???

 

[Deleted member 4993]

My math teacher had explained these graphs (or at least tried to) to me. It got to the point where he was explaining it for like the 10th time and I still didn't get it. So I did what a normal kid would do and just nodded and told him I got it even though I had no idea what's happening. So I'm turning to the internet to help me with this. Can anyone explain the methods to graph these equations? (or just show me pictures of working out, that would help me heaps)

y=x/x^2-9
y=x^2/x^2-16
y=x^2/x-2
y=4-x^2/4+x^2
etc.

All I got so far is that limits and asymptotes are things that you need to know to graph these (yeah, that's practically nothing).

Can you plot:

y = 3x + 5

If yes - please tell us how did you plot that function.

 

[Ishuda]

My math teacher had explained these graphs (or at least tried to) to me. It got to the point where he was explaining it for like the 10th time and I still didn't get it. So I did what a normal kid would do and just nodded and told him I got it even though I had no idea what's happening. So I'm turning to the internet to help me with this. Can anyone explain the methods to graph these equations? (or just show me pictures of working out, that would help me heaps)

y=x/x^2-9
y=x^2/x^2-16
y=x^2/x-2
y=4-x^2/4+x^2
etc.

All I got so far is that limits and asymptotes are things that you need to know to graph these (yeah, that's practically nothing).

In addition, grouping symbols in expressions are very necessary sometimes. For example, for the first equation, did you mean
y = x / (x²-9)
as I suspect or
y = x/x² - 9 = 1/x - 9
which is what you wrote. Sometimes, even though they might not strictly be needed, it is good to use grouping symbols just so there can be no misunderstanding.

 

[stapel]

Can anyone explain the methods to graph these equations? (or just show me pictures of working out, that would help me heaps)

I'm afraid any additional explanation (such as the zillions available online) would look just like what you saw in class and in your textbook. In other words, they'll leave you right where you are: having absolutely no idea what to do. So, instead, we're going to need to see what your thoughts and efforts are, so we can figure out what kind of help you're needing.

\(\displaystyle \mbox{1. }\, y\,=\,\dfrac{x}{x^2\,-\,9}\)

Okay. So you know basic graphing, so you know how to make a T-chart of points, etc. (here) You plugged the denominator into the formulation they gave you to find the asymptotes. (here) You drew these in, and plotted the T-chart points. (here) And... then what?

Please be complete.

By the way, I'm assuming that your functions are meant to be as quoted above and below:

\(\displaystyle \mbox{2. }\, y\, =\, \dfrac{x^2}{x^2\, -\, 16}\)

\(\displaystyle \mbox{3. }\, y\, =\, \dfrac{x^2}{x\, -\, 2}\)

\(\displaystyle \mbox{4. }\, y\, =\, \dfrac{4\, -\, x^2}{4\, +\, x^2}\)

If I have misguessed your intended meaning, kindly please reply with corrections. Thank you!

 

[Mitsukuni]

Can you plot:

y = 3x + 5

If yes - please tell us how did you plot that function.

The gradient is 3 and the y-intercept is 5. So I would just plot a point at (0,5) first. Since the gradient is rise/run, that means that 5/run=3 and the run=5/3 hence the x-intercept is (-5/3,0) because the gradient is positive. From that I would just join the two points.

In addition, grouping symbols in expressions are very necessary sometimes. For example, for the first equation, did you mean
y = x / (x²-9)
as I suspect or
y = x/x² - 9 = 1/x - 9
which is what you wrote. Sometimes, even though they might not strictly be needed, it is good to use grouping symbols just so there can be no misunderstanding.

Sorry bout that. I didn't think that through. It made sense in my head.

I'm afraid any additional explanation (such as the zillions available online) would look just like what you saw in class and in your textbook. In other words, they'll leave you right where you are: having absolutely no idea what to do. So, instead, we're going to need to see what your thoughts and efforts are, so we can figure out what kind of help you're needing.


Okay. So you know basic graphing, so you know how to make a T-chart of points, etc. (here) You plugged the denominator into the formulation they gave you to find the asymptotes. (here) You drew these in, and plotted the T-chart points. (here) And... then what?

Please be complete.

By the way, I'm assuming that your functions are meant to be as quoted above and below:


If I have misguessed your intended meaning, kindly please reply with corrections. Thank you!

I added my working out. And yep that's exactly what I meant