Use the graph of the function f to decide whether the value of the given quantity exists. If it does, find it. (If an answer does not exist, enter DNE.)

Question

(a)    f(0) = ______

(b)    lim f(x) = ______

x→0 

(c)    f(3) = ________

(d)    lim f(x) = _______

 x→3 

Answer 1

(a). f(0) = 1

(b). DNE because there is a gap in the graph when x = 0. The "one-sided" limits are not equal (the limit from the left of f(x) as x approaches 0 is 4 while the limit from the right of f(x) as x approaches 0 is 1).

(c). f(3) DNE

(d). As x approaches 3 from the left and from the right, f(x) approaches 4. So the limit is 4.

Answer 2

a)1

b)The right limit as one approaches 0 is different than the left limit, so there is no limit DME

c)There is an open circle at 3 DNE

d)4 The left limit and the right limit are both 4.