Question 1

Which of the following numbers has a decimal expansion that is non-terminating and non-repeating?

Accepted Answer

√2

Question 2

A hospital monitors the temperature of a patient every hour. Which of the following best describes the relationship between time (in hours) and temperature (in °C)?

Accepted Answer

A function, because each time corresponds to exactly one temperature reading.

Question 3

Which of the following intervals represents all real numbers greater than or equal to 2 and less than 5?

Accepted Answer

[2, 5)

Question 4

Let $$A = \{x \mid 0 \u003c x \u003c 4\}$$ and $$B = \{x \mid 2 \leq x \leq 6\}. $$What is $$A \cap B$$?

Accepted Answer

\{x \mid 2 \leq x \u003c 4\}

Question 5

A chemist records the concentration of a solution as a function of time. If the function is $$C(t) = 5 - 0.2t$$ for $$t \geq 0$$, what is the range of $$C if $$the experiment lasts until $$t = 10$$?

Accepted Answer

[3, 5]

Question 6

Which of the following statements about the function $$f(x) = \frac{1}{x} is $$correct?

Accepted Answer

Its domain is all real numbers except 0.

Question 7

A company models its profit $$P as a $$function of units sold $$x by$$ $$P(x) = 2x - 100. $$What is the minimum number of units that must be sold for the profit to be non-negative?

Accepted Answer

50

Question 8

Which of the following is NOT a property of rational numbers?

Accepted Answer

Their decimal expansions are always non-terminating and non-repeating.

Question 9

Given two points on a line, $$(1, 3)$$ and $$(4, 15)$$, what is the equation of the line passing through them?

Accepted Answer

y = 3x

Question 10

Which of the following sets is described by the interval $$(-\infty, 0]$$?

Accepted Answer

All real numbers less than or equal to 0

Question 11

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

Accepted Answer

[1, \infty)

Question 12

Which of the following best explains why the graph of $$y = x^2$ passes the vertical line test?

Accepted Answer

Each $$x-$$value corresponds to exactly one $$y-$$value.

Question 13

If $$A = \{x \mid x \u003e 2\}$$ and $$B = \{x \mid x \u003c 5\}$$, what is $$A \cap B$$?

Accepted Answer

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

Question 14

A patient’s heart rate is measured every minute and recorded as a function $$H(t)$$, where $$t is $$time in minutes. If $$H(10) = 80$$ and $$H(20) = 90$$, what is the average rate of change of heart rate between $$t=10$$ and $$t=20$$?

Accepted Answer

1 beat per minute per minute

Question 15

Which of the following is an example of a function whose range is $$[0, \infty)$$?

Accepted Answer

f(x) = $$x^2$$

Question 16

A biologist models the population of a bacteria colony as $$P(t) = 100e$$^{0.05t}$$, where t$ is time in hours. Which of the following best describes the domain of P$?

Accepted Answer

All real numbers $$t \geq 0$$

Question 17

Which of the following statements is true about the set of real numbers?

Accepted Answer

It includes all rational and irrational numbers.

Question 18

If the distance between two points on the number line is 7 and one point is at $$-3$$, where could the other point be?

Accepted Answer

4 or -10

Question 19

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

Accepted Answer

[0, \infty)

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

Study Guide - Practice Questions

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