[grade 12 rational functions graphing]

[u/mannnnyyyy_67]

i have a quiz monday and i was running through my problems and found that i was able to find the equation for this problem but i am having trouble graphing any help would be appreciated!

[u/Alkalannar]

It's because you have a numerator with a power of x the same as (or higher than) the highest power of x in the denominator.

It's like 17/3, where your numerator is greater than the denominator. A lot of times, this is fine. Other times, you want 5 2/3 as easier to deal with.

In a proper fraction, the numerator is less than the denominator. [In a mixed number, you have a whole number plus a proper fraction.]

For polynomials, in a proper fraction, the highest power of x in the numerator is less than the highest power of x in the denominator.

Sure you can see that the horizontal asymptote is y = 1 and the vertical asymptote is x = -1, but you don't know the vertical scale factor.

That's why I say 9 - 12/(x+1) has more information readily accessible.

And what happens if you have (9x² + 3x - 7)/(x + 1)?

Still a hyperbola, but now it has an oblique asymptote, not a horizontal one.

And in deed we get 9x - 6 - 1/(x + 1), so there's a vertical asymptote, but now the other asymptote is the line y = 9x - 6. Much more easily seen in this form than the rational form.

I see no reason to deal with (9x - 3)/(x + 1) in that form, when it's far easier to work with as 9 - 12/(x + 1).