Rational Functions

[sunwers]

I am working on rational functions and I'm having problems finding the ordered pairs.


My question has three parts


Step 1 of 3

Given the following rational function: x^2-x+8/x^2-4x+3
Find the vertical asymptotes, if any, for the rational function. Separate multiple equations with a comma.
To get step 1 I factored the denominator and got (x-3)(x-1) giving me x=1 and x=3


Step 2 of 3

Find equations for the horizontal or oblique asymptotes, if any for the rational function. Since the degrees are the same for both denominator and numerator the horizontal or oblique asymptotes is y=1


Step 3 of 3

This is where I'm getting confused


Enter four ordered pairs for the graph of the rational function.

How do I know what x values to plug into the function to get my ordered pairs. I tried plugging in any of the numbers besides the ones above and I got the problem wrong.

Here is what I done


I plugged 2 as the x value and got the ordered pair (2,-10)
I plugged 4 as the x value and got the ordered pair (4,5)
I plugged -1 as the x value and got the ordered pair (-1, 10/13)
I plugged -2 as the x value and got the ordered pair (-2, 7/8)


What am I doing wrong for part 3 of this question?


Thanks and I appreciate your help

 

[JeffM]

I am working on rational functions and I'm having problems finding the ordered pairs.


My question has three parts


Step 1 of 3

Given the following rational function: x^2-x+8/x^2-4x+3
Find the vertical asymptotes, if any, for the rational function. Separate multiple equations with a comma.
To get step 1 I factored the denominator and got (x-3)(x-1) giving me x=1 and x=3


Step 2 of 3

Find equations for the horizontal or oblique asymptotes, if any for the rational function. Since the degrees are the same for both denominator and numerator the horizontal or oblique asymptotes is y=1 This is not quite right. Consider the very simple case of (2x^2 +1)/ x^2. The horizontal asymptote is not 1. Equal degree implies that there is a horizontal asymptote, but not that it is equal to 1. In this case, it is equal to 1, but that is not generally true.


Step 3 of 3

This is where I'm getting confused


Enter four ordered pairs for the graph of the rational function.

How do I know what x values to plug into the function to get my ordered pairs. I tried plugging in any of the numbers besides the ones above and I got the problem wrong.

Here is what I done


I plugged 2 as the x value and got the ordered pair (2,-10)
I plugged 4 as the x value and got the ordered pair (4,5)
I plugged -1 as the x value and got the ordered pair (-1, 10/13)
I plugged -2 as the x value and got the ordered pair (-2, 7/8)


What am I doing wrong for part 3 of this question?


Thanks and I appreciate your help

First, thank you for showing your work for parts 1 and 2.

Second, you need to put parentheses around your numerator and denominator when they contain multiple terms and you are using / to indicate division.

Third, how can we tell what you did wrong in part 3 if you do not show us what you did. I suspect you made careless errors, but I cannot be sure.

 

[DrPhil]

I am working on rational functions and I'm having problems finding the ordered pairs.


My question has three parts


Step 1 of 3

Given the following rational function: (x^2-x+8)/(x^2-4x+3)
Find the vertical asymptotes, if any, for the rational function. Separate multiple equations with a comma.
To get step 1 I factored the denominator and got (x-3)(x-1) giving me x=1 and x=3


Step 2 of 3

Find equations for the horizontal or oblique asymptotes, if any for the rational function. Since the degrees are the same for both denominator and numerator the horizontal or oblique asymptotes is y=1


Step 3 of 3

This is where I'm getting confused


Enter four ordered pairs for the graph of the rational function.

How do I know what x values to plug into the function to get my ordered pairs. I tried plugging in any of the numbers besides the ones above and I got the problem wrong.

Here is what I done


I plugged 2 as the x value and got the ordered pair (2,-10)
I plugged 4 as the x value and got the ordered pair (4,5)...??
I plugged -1 as the x value and got the ordered pair (-1, 10/13)...??
I plugged -2 as the x value and got the ordered pair (-2, 7/8)...??


What am I doing wrong for part 3 of this question?


Thanks and I appreciate your help

You are doing fine. My only comment is that when writing rational expression inline using "/" it is essential to use parentheses to indicate numerator and denominator, to make the order of operations correct.

As to points to choose for part 3, the domain from which you can choose is any x except 1 or 3. I would try to pick one that is <1, one between 1 and 3, and one >3. And x=0 is usually easy to calculate.

I agree with point (2,-10), but not the others. For instance, at x=4, I get (4, 20/3).

 

[sunwers]

First, thank you for showing your work for parts 1 and 2.

Second, you need to put parentheses around your numerator and denominator when they contain multiple terms and you are using / to indicate division.

Third, how can we tell what you did wrong in part 3 if you do not show us what you did. I suspect you made careless errors, but I cannot be sure.

Hi JeffM,

Sorry, I will put my parentheses around my numerator and denominator the next time to indicate division and I will show my complete work. I'm taking online classes and needed some help with a problem. I searched for help and found this forum. This is my first time on a math forum but I will try to post my work better the next time.

You are doing fine. My only comment is that when writing rational expression inline using "/" it is essential to use parentheses to indicate numerator and denominator, to make the order of operations correct.

As to points to choose for part 3, the domain from which you can choose is any x except 1 or 3. I would try to pick one that is <1, one between 1 and 3, and one >3. And x=0 is usually easy to calculate.

I agree with point (2,-10), but not the others. For instance, at x=4, I get (4, 20/3).

Thank you so much for your quick response and I will try another one of my problems and work it by using any x value except the ones as in step 1 and 2. Sorry I will use the parentheses to indicate numerator and denominator the next time. So I can use any x value as long as it isn't the values for the vertical asymptotes and the horizontal or oblique asymptotes, right? I'm going to try another problem and work it as you posted above by using x=0 and by picking a x value greater than, one value in between, and one value less than the two x-intercepts that I get in steps 1 and 2. If I still miss the problem I will be back here to post my work to see what I did wrong. Would it be OK to post it here or do I need to start another thread?

Thanks Again,
Sunwers

 

[stapel]

If I still miss the problem I will be back here to post my work to see what I did wrong. Would it be OK to post it here or do I need to start another thread?

To post follow-ups to this particular exercise, posting in this thread is fine. For new exercises, however, new threads are preferred. Thank you!