Question

lim f(x) as x-> 2- and lim f(x) as x-> 2+ help explain graphs of limits to me?

Answer 1

So how does the graph explain what the limit is?

Answer 2

For \(\large \lim\limits_{x\to 2^{-}} f(x)\), imagine yourself walking on the graph towards x=2 from the left of "x=2"

Answer 3

Okay, that is helpful. Can you explain what the dot on the graph represents?

Answer 4

you're staying on y=f(x)=3, so the left limit is 3 :
\[\large \lim \limits_{x\to2^{-}}f(x) ~~=~~3\]

Answer 5

similarly see if you can find the right limit :
\[\large \lim \limits_{x\to2^{+}}f(x) ~~=~~?\]

Answer 6

-3 ?

Answer 7

Excellent!

the "dot" represents the value of function exactly at x = 2