Rational Function f(x) = 3x / x^2 - x - 6: graph, find asymptote, etc

[Dede 2013]

Hi guys, can you pleases help me with this question


Given the rational function f(x) = 3x / x^2 - x - 6

a) find the intercepts.

b) determine all asymptotes.

c) state where the function is increasing and decreasing.

d) where the slope increasing / decreasing ?


Thanks a lot

 

[stapel]

Given the rational function f(x) = 3x / x^2 - x - 6

Should we assume that grouping symbols have been omitted, and that you really mean "f(x) = (3x)/(x^2 - x - 6)"?

. . . . .\(\displaystyle \displaystyle{f(x)\, =\, \frac{3x}{x^2\, -\, x\, -\, 6}}\)

a) find the intercepts.

What did you get when you plugged zero in for x and solved for y? What did you get when you plugged zero in for y and solved?

b) determine all asymptotes.

What did you get when you checked the zeroes of the denominator? What did you get when you plugged the degrees into the formula they gave you?

c) state where the function is increasing and decreasing.

What did you get when you looked at the graph? (Since you are having trouble with beginning-algebra topics like intercepts, I'm assuming that you haven't gotten to calculus yet.)

Please reply with a clear listing of your efforts so far, or else with specifications about the lesson instruction you are seeking. Thank you!

 

[Dede 2013]

Should we assume that grouping symbols have been omitted, and that you really mean "f(x) = (3x)/(x^2 - x - 6)"?

. . . . .\(\displaystyle \displaystyle{f(x)\, =\, \frac{3x}{x^2\, -\, x\, -\, 6}}\)


What did you get when you plugged zero in for x and solved for y? What did you get when you plugged zero in for y and solved?

When i plugged 0 for x, I got 3x / ( x-3 )( x + 2 ).
and when I plugged 0 for y, I got x is not equal 3 , x is not equal -2 and x is not equal 0 .


What did you get when you checked the zeroes of the denominator? What did you get when you plugged the degrees into the formula they gave you?

When I checked the zeros at the denominator, I got for the vertical asymptote, x=3 and x= -2 . And i don`t know how to get the horizontal asymptote.
And I don`t know what do you mean by " what did you get when you plugged the degrees into the formula ? " because my teacher didn`t mention anything about the degrees.


What did you get when you looked at the graph? (Since you are having trouble with beginning-algebra topics like intercepts, I'm assuming that you haven't gotten to calculus yet.)

I don`t know how to sketch the graph yet , and you are right, cause I haven`t taken the calculus yet. , I`m taking Advanced function, chapter 3.

Please reply with a clear listing of your efforts so far, or else with specifications about the lesson instruction you are seeking. Thank you!

Thanks a lot, really I appreciate that to you

 

[Dede 2013]

1) When i plugged 0 for x, I got 3x / ( x-3 )( x + 2 ).
and when I plugged 0 for y, I got x is not equal 3 , x is not equal -2 and x is not equal 0 .




2) When I checked the zeros at the denominator, I got for the vertical asymptote, x=3 and x= -2 . And i don`t know how to get the horizontal asymptote. :sad:
And I don`t know what do you mean by " what did you get when you plugged the degrees into the formula ? " because my teacher didn`t mention anything about the degrees.




3) I don`t know how to sketch the graph yet :smile: , and you are right, cause I haven`t taken the calculus yet. :smile: , I`m taking Advanced function, chapter 3.



Thanks a lot, really I appreciate that to you :smile:

 

[stapel]

1) When i plugged 0 for x, I got 3x / ( x-3 )( x + 2 ).

If you plugged in zero for x, then why do you still have x's instead of zeroes?

and when I plugged 0 for y, I got x is not equal 3 , x is not equal -2 and x is not equal 0 .

How are you getting "not equals" when you'd started with an equality? Did you review the lesson at the link about finding intercepts?

2) When I checked the zeros at the denominator, I got for the vertical asymptote, x=3 and x= -2 .

Yes.

And i don`t know how to get the horizontal asymptote. :sad:
And I don`t know what do you mean by " what did you get when you plugged the degrees into the formula ? " because my teacher didn`t mention anything about the degrees.

Try the lesson at the link, provided earlier. Also, check your textbook.

3) I don`t know how to sketch the graph yet :smile: , and you are right, cause I haven`t taken the calculus yet. :smile: , I`m taking Advanced function, chapter 3.

Sketching requires only algebra. The comments about calculus related to the derivative's indication of "increasing" versus "decreasing". To learn how to sketch, try studying the lesson at the link.

 

[lookagain]

Given the rational function f(x) = 3x /( x^2 - x - 6)

1) When i plugged 0 for x, I got 3x /(( x -3 )( x + 2 )).

Dede 2013,

you have to have grouping symbols around that denominator, as suggested above.