Question

sketch a graph of function f that satisfies these conditions

Answer 1

.

Answer 2

\[\lim_{x \rightarrow 2} f(x)=-3\]
\[\lim_{x \rightarrow -3^-} f(x)=f(2)=5\]
f is increasing on (-inf, -3)
\[\lim_{x \rightarrow -3^-}f(x)>\lim_{x \rightarrow -3^+}f(x)\]
f is constant on (x, +inf)

Answer 3

it has to satisfy all of those D:

Answer 4

Can you check the following?
f is constant on (x, +inf)

Answer 5

Yes I got that. ^.^

Answer 6

it's an open circle on (2,2) right?

Answer 7

is it "f(x) is constant on (2,+inf)?

Answer 8

no, it just says f. I'm pretty sure f and f(x) mean the same thing, right?

Answer 9

but is "f is constant on (2,+inf)"? (i.e. not (x,+inf) )

Answer 10

yes

Answer 11

I have, right now, an open circle on point (2,2) with a horizontal line going to the right c: that's right, right?

Answer 12

or is it "f is constant on (-3,+inf)"?

Answer 13

f is constant on (2, +inf)

Answer 14

Well, we have
Lim f(x) x->2 = -3, so the horizontal line should be at y=-3.

agree?

Answer 15

wait... why -3?

Answer 16

wait....nvm. I see now

Answer 17

From the first condition,
\(Lim_{x->2} ~~f(x)=-3\)

Answer 18

so far so good?

Answer 19

from f(2)=5 (in the second line),
we have

Answer 20

ok there?

Answer 21

is that vertical line supposed to be there?

Answer 22

The rest of line 2 (lim x->3- = 5 ) gives:

then from the fourth line f is increasing up to x=-3