asymptotes

[wildcornstalk]

find the equations of both the horizontal and vertical asymptotes of the rational function.

a. f(x)=(5x-1)/(x^2+9) i have the vertical as x=-3 and the horizontal as y=0
b. f(x)=(2x^2+8)/(x-1) vertical is x=1 and there is no horizontal.

my question was what exactly do they mean by finding the equation? And also, if I have a graph with points how would I find the equation with only that information. My book doesnt explain very well.

Thank you for your time!

 

[mmm4444bot]

The way things work here is that you first show us what you've done OR you ask specific questions of your own about the stuff you don't understand.

Otherwise, how can we determine where to begin helping you?

Have you learned the meaning of the word asymptote, yet?

Please check the post titled, "Read Before Posting" for guidelines about how to ask for help.

Thank you!

 

[wildcornstalk]

Sorry, I apologize, I was getting frazzled. I have entered my answers along with my questions. Thank you for your time.

 

[JeffM]

find the equations of both the horizontal and vertical asymptotes of the rational function.

a. f(x)=(5x-1)/(x^2+9) i have the vertical as x=-3 and the horizontal as y=0 x = - 3 is NOT a vertical asymptote because ((- 3)[sup:1m0f18mz]2[/sup:1m0f18mz]) + 9 = 9 + 9 = 18, not zero.
b. f(x)=(2x^2+8)/(x-1) vertical is x=1 and there is no horizontal. Yes

my question was what exactly do they mean by finding the equation? And also, if I have a graph with points how would I find the equation with only that information. My book doesnt explain very well. The problem is that the vocabulary to define an asymptote exactly is meaningless to someone in beginning algebra. BUT you will not go far wrong if you think of an asymptote of f(x) as a line that f(x) never touches but approaches more and more closely under certain circumstances. So that asymptotic line has an equation, just like any other line.

 

[mmm4444bot]

find the equations of both the horizontal and vertical asymptotes of the rational function.

This instruction is sloppily worded because it implies that each given function has both horizontal and vertical asymptotes.

Change the phrase "both the" to "any".



what exactly do they mean by finding the equation [of the asymptotes]?

Asymptotes are straight lines. Every line has an equation. For each asymptote, they want you to write its equation.



f(x) = (5x - 1)/(x^2 + 9)

i have the vertical [asymptote] x = -3 and the horizontal [asymptote] y = 0

Vertical asymptotes occur at values of x that make the denominator zero.

As Jeff pointed out, x = -3 does not make the denominator zero.

Try solving x^2 + 9 = 0 again, OR realize that a square is always positive and that adding 9 to a positive number cannot possibly result in zero.

You found the correct equation for the horizontal asymptote: y = 0



b. f(x) = (2x^2 + 8)/(x - 1) vertical [asymptote] x = 1 and there is no horizontal [asymptote]

You are correct.



if I have a graph with points how would I find the equation with only that information

Since all graphs contain points, I'm not sure what you mean by "I have a graph with points". Is there a smooth curve drawn through the points?

If you're trying to ask how to identify asymptotes from the graph of a rational function (versus from analysing the function's algebraic definition), then draw the asymptotes on the graph and look to see where they cross an axis.

Many times, I have heard or read this general claim by instructors and textbook authors alike: "The graph of a function gets close to, but never touches, an asymptote."

As a general statement, this claim is only true for vertical asymptotes.

With respect to the horizontal, a function's graph may touch or even cross back-and-forth over its horizontal asymptote locally. They should make their statement clear that the claim is true only for global behavior (i.e., when x approaches positive or negative infinity).

This is what Jeff meant when he properly qualified his comment with the phrase "under certain circumstances".

Cheers ~ Mark

 

[JeffM]

Yep, it is what I meant, but it was unnecessarily vague.

 

[wildcornstalk]

Hello, I am still unsure of how to find the equation just by looking at the graph.

given the graph of a rational function find the equations of both the vertical and horizontal aymptotes...I am completely clueless.

 

[JeffM]

Hello, I am still unsure of how to find the equation just by looking at the graph.

given the graph of a rational function find the equations of both the vertical and horizontal aymptotes...I am completely clueless.

I must admit that I cannot help you because the question makes no sense as posed. What exactly does the question say? Does the graph SHOW the asymptotes?
Does it show where they cross the a and y axes?

 

[mmm4444bot]

If you're trying to ask how to identify asymptotes from the graph of a rational function … then draw the asymptotes on the graph and look to see where they cross an axis.[/color]

Did you miss my explanation above?

If not, but you chose to ignore it because it makes no sense, then I claim that you need to learn how to ask specific questions about statements that you do not understand.

I could explain further, if I were to discover why you're still stuck. I could even draw you a picture.

I am often willing to go to "great" lengths, but I am not often willing to knowingly waste my time.

(By the way, you did not respond to my previous question about the graph. I cannot see what you are looking at.)

 

[wildcornstalk]

the graph has 2 curved lines, one starting at (-4,1), and curving down through (3, -7). and the other is (3,9) and curves down to (9,1). I am sorry if you feel like you are wasting your time. I truley do not understand. When I think of finding an equation my mind automatically thinks of crazy equations that I could never figure out. I am probably making this harder than it really needs to be...

 

[JeffM]

the graph has 2 curved lines, one starting at (-4,1), and curving down through (3, -7). and the other is (3,9) and curves down to (9,1). I am sorry if you feel like you are wasting your time. I truley do not understand. When I think of finding an equation my mind automatically thinks of crazy equations that I could never figure out. I am probably making this harder than it really needs to be...

The people here are volunteers. They are willing to spend much time on helping a student, but they want the student to spend time on reading all the answers that the volunteers provide and then thinking about those answers.

WE cannot see the graphs that you may be looking at. WE are not sure what is the exact question that has been posed to you. You have to give us the information that we need to help you and show that you are really trying to grasp our answers.

You have given some vital information in your most recent post. You have described in words your graph. What you have not done is to say WHAT equation you are supposed to derive. Is it the equation of the asymptote or of the rational function? Now I am mixed up about the graph. Does it touch the line x = 3 or just get close to it? If it touches that line, does it do so in TWO places? Does the curve running from (-4, 1) toward (3, -7) look like a piece of an upside down U? Does the other curve look like a piece of a U not upside-down?

 

[mmm4444bot]

given the graph of a rational function find the equations of both the vertical and horizontal aymptotes

Here is an example graph for some rational function. I think that they want you to look for asymptotic behavior.

[attachment=2:1uni9i3z]asymptote1.JPG[/attachment:1uni9i3z]



Draw the asymptotes (or simply imagine them in your mind's eye). I drew them in red.

[attachment=1:1uni9i3z]asymptote2.jpg[/attachment:1uni9i3z]



Look to see where the asymptotes cross the axes. I marked these two points with black dots and labeled their coordinates in green.

[attachment=0:1uni9i3z]asymptote3.jpg[/attachment:1uni9i3z]



Write the equations based on the intersections with the axes.

Horizontal asymptote: y = 1

Vertical asymptote: x = 3



That's my best guess.

Cheers ~ Mark

 

[wildcornstalk]

So I am making this more complicated than I need to be, the equations are as simple as x= and y=? thank you all for your help!!

 

[mmm4444bot]

Oh, maybe you forgot the following, from back when you learned about graphing lines.

All vertical lines have equations of the form x = n, where symbol n represents any Real number, and all horizontal lines have equations of the form y = n.

In each case, n is the axis-intercept, too.

Vertical lines have x-intercept (n, 0) and horizontal lines have y-intercept (0, n). When n = 0, the line coincides with the axis.