Question

find the domain, points of discontinuity, and x and y intercepts of each rational function. determine whether the discontinuities are removable or non removable.
y= x^2 + 2x/ x^2 +2

Answer 1

\[y={x^2+2x\over x^2+2}\]?

Answer 2

yes, sorry i don't know how to do that line thing

Answer 3

it's okay, just next time use parentheses
y=(x^2+2x)/(x^2+2)
would have been much clearer

anyway, first is domain:
are there any values for which this function is undefined?

Answer 4

i don't think so.

Answer 5

right, the denominator is never zero, we have no negative square roots or logarithms
so it is defined for all reals...

Answer 6

okay

Answer 7

and i think the points of discontinuity are x=1, and x =6

Answer 8

?

Answer 9

why?

Answer 10

oh no sorry. i was looking at wrong problem

Answer 11

discontinuity:
it's defined for all reals, and has no "jump" points, so it is continuous everywhere

Answer 12

do you know how to find x and y intercepts?

Answer 13

yeah don't you set x= to 0 and y = to 0 and substitute it into the equation ?

Answer 14

exactly

Answer 15

so there are no points of discontinuity then?

Answer 16

no
if the function is defined everywhere, and is not a step function, then it is (as far as I know) always continuous everywhere

Answer 17

okay

Answer 18

that makes the third question trivial, since we have no discontinuities to talk about
so I guess we're done :)

Answer 19

or fifth Q or whatever it was

Answer 20

okay. thanks.

Answer 21

anytime :)

Answer 22

hey would you kknow how to factor x^2+2 or x^2 + 9 i forgot?

Answer 23

neither can be factored by "traditional" means
x^2-9=(x+3)(x-3)
^^^^^^^^^perhaps that is what you are thinking of?

Answer 24

find the vertical asymptotes and holes for the graph of each rational function.
y=(x+5) / (x^2+9)
and when i do these types of problems usually i factor it out to get the asymptotes but idk how to factor the bottom. please help?