Question 1

Given the graph, the function is continuous at x = 0.

Accepted Answer

true

Answer

false

Question 2

Given the graph, the function is continuous at x = 1.

Accepted Answer

false

Answer

true

Question 3

Given the graph, the function is continuous at x = 2.

Accepted Answer

true

Answer

false

Question 4

Given the graph, the function is continuous at x = 3.

Accepted Answer

false

Answer

true

Question 5

Given the graph, the function is continuous at x = 5.

Accepted Answer

false

Answer

true

Question 6

Given the graph, the function is continuous on the interval [-11,-6].

Accepted Answer

false

Answer

true

Question 7

Given the graph, the function is continuous on the interval [-2,6).

Accepted Answer

false

Answer

true

Question 8

Given the graph, the function is continuous on the interval (-4,-2]?.

Accepted Answer

true

Answer

false

Question 9

Given the graph, the function is continuous on the interval [4,10).

Accepted Answer

false

Answer

true

Question 10

Given the graph, the function is continuous on the interval (-8,-4).

Accepted Answer

true

Answer

false

Question 11

Which is NOT a condition for a function to be continuous at x = a?

Accepted Answer

The limits of the function exist but they are not equal to the function value at x = a.

Answer

The limit of the function as 𝑥 approaches 𝑎 exists.

Answer

The limit of the function as 𝑥 approaches 𝑎 is equal to the function value at 𝑥 = 𝑎

Answer

The function is defined at 𝑥 = 𝑎; that is, 𝑓(𝑎) equals a real number.

Question 12

Which statement is true about the function on the graph?

Accepted Answer

The function is discontinuous at x = 4.

Answer

It is continuous everywhere.

Answer

The limits of the function at x = 4 are equal.

Answer

The function is continuous on the interval [2,5].

Question 13

In what interval is $f\left(x\right)=\sqrt{-2x+5}$ continuous?

Accepted Answer

$\mathbb{R}\ except\ \left\{\frac{5}{2}\right\}$

Answer

$\mathbb{R}\ except\ \left\{\frac{5}{2}\right\}$

Answer

$\mathbb{R}\ except\ \left\{\frac{5}{2}\right\}$

Answer

$\mathbb{R}\ except\ \left\{\frac{5}{2}\right\}$

Question 14

For which of the following does $f\left(x\right)=\sqrt{-2x+5}$ exist?

Accepted Answer

I and II only

Answer

I only

Answer

II only

Answer

All of the above.

Question 15

Which of the following is continuous everywhere?

Accepted Answer

$\mathbb{R}\ except\ \left\{\frac{5}{2}\right\}$

Answer

$\mathbb{R}\ except\ \left\{\frac{5}{2}\right\}$

Answer

$\mathbb{R}\ except\ \left\{\frac{5}{2}\right\}$

Answer

$\mathbb{R}\ except\ \left\{\frac{5}{2}\right\}$

Question 16

Which of the following is true about the function 𝑓 if $f\left(x\right)=\sqrt{-2x+5}$ ?

I. 𝑓 is continuous at x = 1

II. The graph of 𝑓 has a vertical asymptote at x = 1

III. The graph of 𝑓 has a horizontal asymptote at $y=\frac{1}{2}$

Accepted Answer

III only

Answer

I only

Answer

II only

Answer

All of the above

Question 17

When does a limit exist?

Accepted Answer

The left-hand and right-hand limits at c must be equal.

Answer

None of the choices given

Answer

The left-hand limit must exist for 𝑥 = 𝑐.

Answer

The right-hand limit must exist for 𝑥 = 𝑐.

Question 18

It is a type of discontinuity in which the $f\left(x\right)=\sqrt{-2x+5}$ and $\lim_{x o a^+}f\left(x
ight)$ both exists, but $\lim_{x o a^-}f\left(x
ight)
e\lim_{x o a^+}f\left(x
ight)$

Accepted Answer

Jump

Answer

Infinite

Answer

Removable

Answer

None of the given choices

Question 19

The discontinuity of the function shown on the graph is __________.

Accepted Answer

Jump

Answer

Removable

Answer

None of the given choices

Answer

Infinite

Question 20

In the six basic trigonometric functions, which are continuous over all real numbers? Which are not? (Click a trigonometric function, then click the category where it belongs)

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