Q: Which of the following sets is the set of all real numbers $$x$$ such that $$1 \u003c x \\\\leq 5$$?

$$\\{x \\mid 1 \u003c x \\leq 5\\}$$

Q: Which of the following statements about the set of rational numbers $$\\mathbb{Q} is $$TRUE?

Every rational number can be written as a fraction $$\\frac{p}{q}$$ where $$p$$ and $$q$$ are integers and $$q \\neq 0.$$

Q: A function $$f is $$defined on $$[0, \\infty) by$$ $$f(x) = \\sqrt{x}. $$Which of the following is TRUE?

The domain of $$f is$$ $$[0, \\infty)$$ and the range is $$[0, \\infty).$$

Q: Which of the following is an example of a piecewise-defined function?

$$f(x) = \\begin{cases} x^2$ & x \\geq 0 \\\\ -x & x \u003c 0 \\end{cases}$$

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

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

Question 1

Which of the following sets is the set of all real numbers $$x$$ such that $$1 \u003c x \\leq 5$$?

Accepted Answer

$$\{x \mid 1 \u003c x \leq 5\}$$

Question 2

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

Accepted Answer

$$\{x \mid x \geq 2\}$$

Question 3

Which of the following statements about the set of rational numbers $$\mathbb{Q} is $$TRUE?

Accepted Answer

Every rational number can be written as a fraction $$\frac{p}{q}$$ where $$p$$ and $$q$$ are integers and $$q \neq 0.$$

Question 4

Let $$f(x) = 2x + 3. $$Which of the following best describes the graph of $$f$$?

Accepted Answer

A straight line with slope $$2$$ and $$y-$$intercept $$3.$$

Question 5

Which of the following intervals represents all real numbers $$x$$ such that $$-2 \u003c x \leq 4$$?

Accepted Answer

$$(-2, 4]$$

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 is NOT a function?

Accepted Answer

The relation $$y^2 = x$

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 best describes the range of the function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$\{y \mid y \geq 0\}$$

Question 10

A real-world scenario: The temperature $$T (in $$degrees Celsius) at time $$t (in $$hours) is given by $$T(t) = 10 + 5\sin\left(\frac{\pi}{12}t\right). $$What is the maximum temperature during the day?

Accepted Answer

$$15$$ degrees Celsius

Question 11

Which of the following decimal expansions represents a rational number?

Accepted Answer

$$0.333333\ldots$$

Question 12

Suppose $$f(x) = x^2$ - 4x + 3. $$For which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

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

Question 13

Which of the following best describes the set $$\{x \mid x^2$ \u003c 9\}$$?

Accepted Answer

$$(-3, 3)$$

Question 14

A function $$f is $$defined on $$[0, \infty) by$$ $$f(x) = \sqrt{x}. $$Which of the following is TRUE?

Accepted Answer

The domain of $$f is$$ $$[0, \infty)$$ and the range is $$[0, \infty).$$

Question 15

Which of the following is the correct definition of the distance between two real numbers $$a$$ and $$b$$?

Accepted Answer

$$|a - b|$$

Question 16

Which of the following is an example of a piecewise-defined function?

Accepted Answer

$$f(x) = \begin{cases} x^2$ & x \geq 0 \\ -x & x \u003c 0 \end{cases}$$

Question 17

A medical test result is modeled by the function $$R(t) = 100e$$^{-0.05t}$$, where t$ is the time in hours since the test was administered. What is the value of R(0$$)$$?

Accepted Answer

$$100$$

Question 18

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 19

Which of the following is the correct interval notation for the set $$\{x \mid x \geq 2\}$$?

Accepted Answer

$$[2, \infty)$$

Question 20

A population of bacteria is modeled by $$P(t) = 500 \cdot 2^t$$, where $$t is $$the time in hours. What is the population after $$3$$ hours?

Accepted Answer

$$4000$$

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

Study Guide - Practice Questions

Study Guide - Flashcards