From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!

Continuity of Functions: A Hop, Skip, and a Jump Quiz

Think you’ve got your head wrapped around Continuity of Functions? Put your knowledge to the test. Good luck — the Stickman is counting on you!
Q.
• Consider the following statements:

I. f(c) is defined

II.  exists

III.

We say "f is continuous at c" if which of the following statements hold?

I
II
I, II
I, II, III
Q. Which of the statements is true about the function f graphed below?

f is discontinuous at x = 1 because f(1) does not exist.

f is discontinuous at x = 1 because  does not exist.

f is discontinuous at x = 1 because
f is continuous at x = 1.

Q. Let

Identify all points at which f is discontinuous.

x = 0, x = 1

x = 1, x = 2

x = 0, x = 2

x = 0, x = 1, x = 2

Q. Identify all points at which f is discontinuous.

x = 1, x = -2
x = 1, x = 3
x = -2, x = 3
x = 1, x = -2, x = 3

Q. On which of the following intervals is f continuous?

(-1, 1)
(0, 3)
(2, 4)
(0, 4)
Q. On which of the following intervals is f discontinuous?

(-10, 2)
(2, 4)
(3, 4)
(3, 5)
Q. Let

On which of the following intervals is f continuous?

(-2, 0)
(1, 5)
(4, 6)
(-1, 1)
Q. Let

On which of the following intervals is f(x) continuous?

(-1, 1)
[0, 1)
(-1, 0]
[-1, 1]
Q. Let f(x) = x + 1 and g(x) = x – 1. Which of the following statements is false?

The function  is continuous at x = 1.

The function  is continuous at x = -1.

The function f + g is continuous at x = 1.

The function  is continuous at x = 1.

Q. Which of the following functions is not continuous?

f(x) = ex

g(x) = sin(x)

h(x) = tan(x)

m(x) = x2 – 2x + 3