Q: Which of the following sets is the set of all real numbers $$x$$ such that $$1 \u003c x \u003c 4$$?

$$\\{x \\mid 1 \u003c x \u003c 4\\}$$

Q: Which of the following is NOT a function?

The rule that assigns to each $$x$$ the value $$\\pm \\sqrt{x}$$ for $$x \\geq 0$$

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

$$\\{x \\mid x \\neq 2, x \\neq -2\\}$$

Q: Which of the following is the correct set notation for the set of all real numbers except $$0$$?

$$\\mathbb{R} \\setminus \\{0\\}$$

Q: Which of the following best describes a rational number?

A number that can be written as $$\\frac{p}{q}$$, where $$p$$ and $$q$$ are integers and $$q \\neq 0$$

Question 1

Which of the following sets is the set of all real numbers $$x$$ such that $$1 \u003c x \u003c 4$$?

Accepted Answer

$$\{x \mid 1 \u003c x \u003c 4\}$$

Question 2

Which of the following numbers has a finite decimal expansion?

Accepted Answer

$$\frac{2}{5}$$

Question 3

Suppose $$f(x) = 2x + 3. $$What is the slope of the graph of $$f$$?

Accepted Answer

$$2$$

Question 4

The distance along the number line between two numbers $$a$$ and $$b is $$given by:

Accepted Answer

$$|a - b|$$

Question 5

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

Accepted Answer

$$x \geq 2$$

Question 6

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

Accepted Answer

$$\{x \mid x \neq 1\}$$

Question 7

Which of the following statements about real numbers is TRUE?

Accepted Answer

Every real number can be represented as a possibly unending decimal expansion.

Question 8

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 9

Which of the following is NOT a function?

Accepted Answer

The rule that assigns to each $$x$$ the value $$\pm \sqrt{x}$$ for $$x \geq 0$$

Question 10

A real-world example: The temperature $$T (in $$degrees Celsius) at time $$t (in $$hours) is given by $$T(t) = 20 + 5\sin(\pi t/12). $$What is the maximum temperature during the day?

Accepted Answer

$$25$$

Question 11

Which of the following intervals represents all real numbers $$x$$ such that $$-2 \leq x \u003c 3$$?

Accepted Answer

$$[-2, 3)$$

Question 12

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

Accepted Answer

$$\{x \mid x \neq 2, x \neq -2\}$$

Question 13

Which of the following is the correct set notation for the set of all real numbers except $$0$$?

Accepted Answer

$$\mathbb{R} \setminus \{0\}$$

Question 14

If $$f(x) = 3x - 2$$ and $$f(a) = 10$$, what is the value of $$a$$?

Accepted Answer

$$4$$

Question 15

Which of the following best describes a rational number?

Accepted Answer

A number that can be written as $$\frac{p}{q}$$, where $$p$$ and $$q$$ are integers and $$q \neq 0$$

Question 16

Which of the following is the correct formula for a linear function?

Accepted Answer

$$f(x) = mx + b$$

Question 17

A function $$f is $$defined by $$f(x) = x^2$ - 4x + 3. $$For which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1 or$$ $$x = 3$$

Question 18

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

Accepted Answer

The set of all possible values $$f(x)$$ can take as $$x$$ varies over the domain

Question 19

Suppose $$f(x) = \sqrt{9 - x^2$}. $$What is the domain of $$f$$?

Accepted Answer

$$-3 \leq x \leq 3$$

Question 20

Which of the following is a correct interpretation of the vertical line test?

Accepted Answer

A graph represents a function if and only if no vertical line intersects the graph more than once.

MATH 221: First Semester Calculus – Study Notes (Chapter 1: Numbers and Functions)

Study Guide - Practice Questions

Study Guide - Flashcards