Question

Where is the following function discontinuous? How can it be defined at the points of discontinuity to make it continuous?

f(x)=(x^3+3x^2+2x)/(x^2+2x)

Answer 1

did you factor? top and bottom? once you do, before you cancel, see what make the bottom 0. those are point(s) that will be excluded from the domain of the original. call them fred and ethel. see what the limit is at fred and ethel and define the function to be that value(the limit) when x = fred and when x = ethel.

Answer 2

So after factoring it would be \[f(x)=\frac{ x(x+2)(x+1) }{x(x+2) }\] the problem would be undefined at 0 and -2, right?

Answer 3

right... now cancel the common factors... what's left?

Answer 4

(x+1)

Answer 5

so when x = 0, what's x+1?

Answer 6

1

Answer 7

and when x = -2?

Answer 8

-1

Answer 9

which means the limit does not exist

Answer 10

right! so your function is discontiuous at x = -2 and x = 0. you would need the function to be defined to be -1 when x = -2 and 1 when x = 0, then it would be continuous.

Answer 11

thank you!

Answer 12

you're welcome. you get it now?

Answer 13

yes