Q: Suppose $$f(x) = x^2$ + 1. $$What is the domain and range of $$f$$?

Domain: $$\\mathbb{R}$$, Range: $$[1, \\infty)$$

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

$$\\mathbb{R} \\setminus \\{2\\}$$

Q: Which of the following sets contains all rational numbers between $$0$$ and $$1$$?

$$\\{x \\mid 0 \u003c x \u003c 1, x \\in \\mathbb{Q}\\}$$

Question 1

Which of the following sets contains all real numbers $$x$$ such that $$x^2$$ \u003c 4$$?

Accepted Answer

$$(-2, 2)$$

Question 2

Suppose $$f(x) = x^2$ + 1. $$What is the domain and range of $$f$$?

Accepted Answer

Domain: $$\mathbb{R}$$, Range: $$[1, \infty)$$

Question 3

A function $$f is $$defined by $$f(x) = \sqrt{x-3}. $$What is the domain of $$f$$?

Accepted Answer

$$[3, \infty)$$

Question 4

Which of the following statements about the graph of a function is TRUE?

Accepted Answer

It passes the vertical line test.

Question 5

Let $$f(x) = 2x + 5. $$What is the slope and $$y-$$intercept of the graph of $$f$$?

Accepted Answer

Slope: $$2$$, $$y-$$intercept: $$5$$

Question 6

Which of the following is NOT a real number?

Accepted Answer

$$\sqrt{-1}$$

Question 7

A medical researcher models the concentration of a drug in the bloodstream by $$C(t) = 5e$$^{-0.2t}$$, where t$ is time in hours. What is the initial concentration?

Accepted Answer

$$5$$

Question 8

Which of the following intervals represents all $$x$$ such that $$|x| \u003c 3$$?

Accepted Answer

$$(-3, 3)$$

Question 9

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

Accepted Answer

$$\mathbb{R} \setminus \{2\}$$

Question 10

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

Accepted Answer

$$|a - b|$$

Question 11

Suppose you are given the set $$A = \{x \mid x \u003e 1\}$$ and $$B = \{x \mid x \u003c 3\}. $$What is $$A \cap B$$?

Accepted Answer

$$(1, 3)$$

Question 12

A chemical reaction rate is modeled by $$R(t) = 10 - t^2$ for t$ in $$[0, 3]$$. What is the maximum rate and at what time does it occur?

Accepted Answer

Maximum rate: $$10 at$$ $$t = 0$$

Question 13

Which of the following is the correct set notation for all real numbers $$x$$ such that $$x \geq 0$$?

Accepted Answer

$$[0, \infty)$$

Question 14

A population of bacteria grows according to $$P(t) = 1000e$$^{0.05t}$$. What is the population after t = 20$ hours?

Accepted Answer

$$1000e^{1}$$ \approx 2718$$

Question 15

Which of the following is a linear function?

Accepted Answer

$$f(x) = 3x - 7$$

Question 16

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

Accepted Answer

$$[-3, 3]$$

Question 17

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 $$f(x).$$

Question 18

A real-world application: The height $$h (in $$meters) of a ball thrown upward is given by $$h(t) = 20t - 4.9t^2$. What is the maximum height reached by the ball?

Accepted Answer

$$20.41$$ meters

Question 19

Which of the following sets contains all rational numbers between $$0$$ and $$1$$?

Accepted Answer

$$\{x \mid 0 \u003c x \u003c 1, x \in \mathbb{Q}\}$$

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

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