Question

how to graph general rational functions?
like y=2x/x^2-1

Answer 1

first, you'll need to know the asymptotes. in this case, as\(x^2 -1 \neq 0\)
\(x= \pm 1\) is the asymptotes.

Answer 2

then you'll need to know the max/min points. use differentiation to find them and plot the points.

Answer 3

so like two and 1? also how do you know or like get if it has a 0 or not?

Answer 4

\(y=2x(x^2-1)^{-1}\)
\(y'=2(x^2-1)^{-1} -2x(x^2-1)^{-2} \)

Answer 5

how did you get the two and 1?

Answer 6

umm cuz there's a 2 and a 1? i was just trying but i knew it probably wasn't that easy

Answer 7

nope. you'll have to use the global max/min test to find the points.
at the max points, their gradients=0, so y'=0.

Answer 8

is it because it's 2x it's zero? like cuz of the x or if not then plz explain that that global max/min test is cuz i don't get it

Answer 9

at the max point,

Answer 10

wait. is this a precalculus question?

Answer 11

? that looks higher than 0 aka the 0 on the y axis unless that has somethin to do with the gradient cuz idk what that is and yes this is a precalc question though my algebra book has it in there.

Answer 12

I put the question here and like in a few other math places cuz i thought maybe someone would answer my question cuz when i put it in only one i was waiting for like ten minutes and nobody answered

Answer 13

okay, then you might want to know that it should look like this.
without calculus, you'll just have to memorise the shape and plot points.