Q: A function $$f is $$given by $$f(x) = \frac{1}{x^2$ - 4}. $$What is the domain of $$f$$?

$$x \in \mathbb{R}, x \neq 2, x \neq -2$$

Q: Which of the following is a correct example of set notation for the set of all $$x$$ such that $$x is a $$rational number?

$$Q = \{x \mid x \text{ is rational}\}$$

Q: Which of the following is the correct set notation for the union of sets $$A$$ and $$B$$?

$$A \cup B = \{x \mid x \text{ belongs to } A \text{ or } B\}$$

Question 1

Which of the following sets contains all real numbers $$x$$ such that $$1 \u003c x \u003c 6$$?

Accepted Answer

$$B = \{x \mid 1 \u003c x \u003c 6\}$$

Question 2

Which of the following is the correct definition of the domain of a function $$f$$?

Accepted Answer

The set of all real numbers $$x$$ for which $$f(x) is $$defined.

Question 3

Suppose $$f(x) = \sqrt{x-2}. $$What is the domain of $$f$$?

Accepted Answer

$$x \geq 2$$

Question 4

A function $$f is $$given by $$f(x) = \frac{1}{x^2$ - 4}. $$What is the domain of $$f$$?

Accepted Answer

$$x \in \mathbb{R}, x 
eq 2, x 
eq -2$$

Question 5

Which of the following statements about the vertical line test is correct?

Accepted Answer

A graph represents a function if and only if every vertical line intersects the graph at most once.

Question 6

Given the function $$f(x) = mx + b$$, which of the following statements is true?

Accepted Answer

The graph of $$f is a $$straight line with slope $$m$$ and $$y-$$intercept $$b.$$

Question 7

If $$f(x) = x^2$, what is the range of f$?

Accepted Answer

$$[0, \infty)$$

Question 8

Which of the following is NOT a real number?

Accepted Answer

$$\sqrt{-1}$$

Question 9

Suppose you want to find the distance between two points $$a$$ and $$b on $$the real number line. Which formula should you use?

Accepted Answer

$$|a - b|$$

Question 10

Which of the following sets is the interval $$[2, 5)$$?

Accepted Answer

$$\{x \mid 2 \leq x \u003c 5\}$$

Question 11

A function $$f is $$defined by $$f(x) = \frac{1}{x}. $$What is the domain of $$f$$?

Accepted Answer

$$x \in \mathbb{R}, x 
eq 0$$

Question 12

Which of the following is a correct example of set notation for the set of all $$x$$ such that $$x is a $$rational number?

Accepted Answer

$$Q = \{x \mid x 	ext{ is rational}\}$$

Question 13

If $$f(x) = \sqrt{x}$$, which of the following is true about the domain and range of $$f$$?

Accepted Answer

Domain: $$x \geq 0$$, Range: $$y \geq 0$$

Question 14

Which of the following is the correct set notation for the union of sets $$A$$ and $$B$$?

Accepted Answer

$$A \cup B = \{x \mid x 	ext{ belongs to } A 	ext{ or } B\}$$

Question 15

A real-world application: The distance $$d (in $$meters) an object falls in $$t$$ seconds under gravity (ignoring air resistance) is given by $$d = 4.9t^2$. What is the domain of this function?

Accepted Answer

$$t \geq 0$$

Question 16

Which of the following is a correct statement about rational numbers?

Accepted Answer

A rational number can be written as $$\frac{p}{q}$$ where $$p$$ and $$q$$ are integers and $$q 
eq 0.$$

Question 17

Which of the following is the correct formula for the slope $$m of a $$line passing through points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 18

Which of the following is the correct definition of a function?

Accepted Answer

A rule which assigns to each $$x in $$the domain exactly one value $$f(x).$$

MATH 221 First Semester Calculus: Numbers, Functions, and Graphs

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