I have a question regarding rational functions

[abel muroi]

I don't need help with a problem this time, i just need an answer to a question.

When graphing rational functions, do you think I should use the rational function in FACTORED form to graph the function? for example..

(2x² + 7x - 4)/(x² + x - 2) = (2x² - 1)(x + 4)/ (x + 2)(x - 1)

Should i use (2x² + 7x - 4)/(x² + x - 2) to find all the points in the graph? or should i use (2x² - 1)(x + 4)/ (x + 2)(x - 1)?

 

[Ishuda]

I don't need help with a problem this time, i just need an answer to a question.

When graphing rational functions, do you think I should use the rational function in FACTORED form to graph the function? for example..

(2x² + 7x - 4)/(x² + x - 2) = (2x² - 1)(x + 4)/ (x + 2)(x - 1)

Should i use (2x² + 7x - 4)/(x² + x - 2) to find all the points in the graph? or should i use (2x² - 1)(x + 4)/ (x + 2)(x - 1)?

It shouldn't make any difference but if there is a common factor it might make it, in some sense, easier to graph if the common factors were canceled.

 

[abel muroi]

It shouldn't make any difference but if there is a common factor it might make it, in some sense, easier to graph if the common factors were canceled.

Thank you for the response,

so what if i only factored the denominator of the rational function and not the numerator, it won't make a difference right?

 

[Ishuda]

Thank you for the response,

so what if i only factored the denominator of the rational function and not the numerator, it won't make a difference right?

It shouldn't but you need to be sure to express the results properly [that is in the context of what you are using]. For example, suppose we had f(x) = 1/(x²-1), so that f(2)=1/3. If I wrote this as
f(x) = 1/(x-1)(x+1)
then that would generally be interpreted as
f(x) = [ 1 / (x-1) ] * (x+1)
with f(2) = 3 and not as
1 / [ (x-1) * (x+1) ]
with f(2)=1/3 which is what you need.

 

[stapel]

I don't need help with a problem this time, i just need an answer to a question.

When graphing rational functions, do you think I should use the rational function in FACTORED form to graph the function? for example..

(2x² + 7x - 4)/(x² + x - 2) = (2x² - 1)(x + 4)/ (x + 2)(x - 1)

Should i use (2x² + 7x - 4)/(x² + x - 2) to find all the points in the graph? or should i use (2x² - 1)(x + 4)/ (x + 2)(x - 1)?

In factored form, you can very easily find the x-intercepts (being the zeroes of the numerator) and the vertical asymptotes (being the zeroes of the denominator). Otherwise, I don't think it much matters.

 

[Deleted member 4993]

In CLD era (Calculator-less-days, when I did these problems ) finding the asymptotes and the intercepts were essential for graphing by hand. Also factorization makes you aware of any removable discontinuities.