Which of the following statements are true of the function y = f(x) graphed here?
a) lim + 𝑓(𝑥) = 1
b) lim− 𝑓(𝑥) = 0
c) lim− 𝑓(𝑥) = 1
d) lim− 𝑓(𝑥) = lim+ 𝑓(𝑥)
e) lim 𝑓(𝑥) exists
f) lim 𝑓(𝑥) = 0
g) lim 𝑓(𝑥) = 1
h) lim 𝑓(𝑥) = 1
i) lim 𝑓(𝑥) = 0
𝑥 → −1
𝑥→0
𝑥→0
𝑥→0
𝑥→0
𝑥→ 0
𝑥→1
𝑥→0
𝑥→ 0
𝑥→1
j) lim− 𝑓(𝑥) = 2
𝑥→2
Which of the following statements are true of the function y = f(x) graphed here?
a) lim+ 𝑓(𝑥) = 1
b) lim 𝑓(𝑥) does not exist
c) lim 𝑓(𝑥) = 2
d) lim− 𝑓(𝑥) = 2
e) lim+ 𝑓(𝑥) = 1
f) lim 𝑓(𝑥) DNE
𝑥→1
𝑥→1
g) lim+ 𝑓(𝑥) = lim− 𝑓(𝑥)
𝑥→0
𝑥→0
h) lim 𝑓(𝑥) exists at every c in (-1, 1)
𝑥→𝑐
i) lim 𝑓(𝑥) exists at every c in (1, 3)
𝑥→𝑐
𝑥→2
𝑥→1
𝑥→2
𝑥→ 1
Answers
True/False
#1
(a) true
(f) true
(b) true
(g) false
(c) false
(h) false
(d) true
(i) false
(e) false
(j) false
#2
(a) true
(f) true
(b) false
(g) true
(c) false
(h) true
(d) true
(i) true
(e) true
Continuity
#1
f(x) is continuous at x = -1, 2
f(x) is discontinuous at x = 0, 1
#2
f(x) is continuous at x = -1, 0, 3
f(x) is discontinuous at x = 1, 2