Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$x \geq 2$$

Question 2

Given the function $$f(x) = \frac{1}{x-3}$$, what type of discontinuity does it have at $$x=3$$?

Accepted Answer

Infinite discontinuity

Question 3

If $$f(x) is $$continuous on $$[a, b]$$ and $$N is $$any number between $$f(a)$$ and $$f(b)$$, which theorem guarantees the existence of $$c in$$ $$(a, b)$$ such that $$f(c) = N$$?

Accepted Answer

Intermediate Value Theorem

Question 4

Evaluate $$\lim_{x 	o 2} \frac{x^2$ - 4}{x - 2}.$$

Accepted Answer

4

Question 5

Which of the following statements about the function $$f(x) = \sin(x) is $$true?

Accepted Answer

Its domain is all real numbers and its range is $$[-1, 1]$$

Question 6

Suppose $$\lim_{x 	o 1^-} f(x) = 2$$ and $$\lim_{x 	o 1^+} f(x) = 3. $$What type of discontinuity does $$f(x)$$ have at $$x=1$$?

Accepted Answer

Jump discontinuity

Question 7

Which of the following limits represents the left-hand limit of $$f(x) as$$ $$x$$ approaches $$c$$?

Accepted Answer

$$\lim_{x 	o c^-} f(x)$$

Question 8

If $$f(x)$$ and $$h(x)$$ both approach $$L as$$ $$x$$ approaches $$c$$, and $$f(x) \leq g(x) \leq h(x)$$ for all $$x$$ near $$c$$, what can be concluded about $$\lim_{x 	o c} g(x)$$?

Accepted Answer

$$\lim_{x 	o c} g(x) = L$$

Question 9

Which of the following is NOT a condition for continuity of $$f(x) at$$ $$x = c$$?

Accepted Answer

$$f(x) is $$differentiable at $$x = c$$

Question 10

Evaluate $$\lim_{x 	o 0} \frac{\sin(x)}{x}.$$

Accepted Answer

1

Question 11

Which of the following best describes a removable discontinuity?

Accepted Answer

The limit exists but the function value is either not defined or not equal to the limit

Question 12

For the function $$f(x) = \frac{x^2$ - 9}{x - 3}$$, what is the value of $$\lim_{x 	o 3} f(x)$$?

Accepted Answer

6

Question 13

Which of the following is the correct notation for the limit of $$f(x) as$$ $$x$$ approaches $$c$$?

Accepted Answer

$$\lim_{x 	o c} f(x)$$

Question 14

If $$f(x) = x^2$ and g(x) = 2x$, what is $$\lim_{x 	o 0} \frac{f(x)}{g(x)}$$?

Accepted Answer

0

Question 15

Which of the following functions has a horizontal asymptote at $$y=0$$?

Accepted Answer

$$f(x) = \frac{1}{x}$$

Question 16

If $$f(x) is $$continuous on $$[1, 4]$$ and $$f(1) = -2$$, $$f(4) = 5$$, which of the following must be true?

Accepted Answer

There exists $$c in$$ $$(1, 4)$$ such that $$f(c) = 0$$

Question 17

Which of the following is an example of an indeterminate form when evaluating limits?

Accepted Answer

$$\frac{0}{0}$$

Question 18

The graph of $$y = f$$^{-1}$$(x) is a $$reflection of the graph of $$y = f(x)$$ across which line?

Accepted Answer

$$y = x$$

Question 19

Which of the following best describes the range of the function $$f(x) = e^x$$?

Accepted Answer

$$(0, \infty)$$

Pre-Calculus Foundations for Calculus: Functions, Limits, and Continuity

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