Question

Does f(x)= IxI <--x inside absolute value bars
----- <-- over/divided by
x <-- just normal x haha

have right or left limits at 0? And is f(x) continuous?

how can i determine this? :) thanks!!!

Answer 1

Here is the graph:
http://www.wolframalpha.com/input/?i=f%28x%29%3D |x|%2Fx

Answer 2

erm not too sure...

would this be an undefined limit? since it has both left and right limits at 0? (or that's what i'm thinking at least.. not sure if that's right though.. )

Answer 3

and this would NOT be a continuous graph right?

Answer 4

oh wait.. the right and left hand limits are the same correct? so that wouldn't be undefined... :/ i think... but i forgot, if both are the same, what does that mean?

Answer 5

oh and i forgot to say why i think it's not continuous haha.. i think it's not continuous because it shoots up along the y axis... is that right? :/

Answer 6

Break up the abs value:

on the left of zero it's \[\Large \frac{ -x }{ x }\](since abs value is really just y=-x when x<0 )

on the right of zero \[\Large \frac{ x }{ x }\]

Answer 7

Simplify each of those to get left and right hand limits.

Answer 8

ohh okay awesome!!

so would it be left limit = -1 and right limit = 1 ?

Answer 9

oh so those are right? :O

Answer 10

lol yes :D

Answer 11

haha yay! :)

wait and so it's not continuous right? :)

Answer 12

because when it reaches 0, it goes straight up/down along the y axis?

not sure if my thinking is right here haha

Answer 13

not sure why it keeps saying I'm typing lol

Answer 14

A function can't be continuous if left and right hand limits don't match, and it's also undef. when x=0

Answer 15

ohh okay awesome!! thank you!!