Question 1

Which of the following numbers has a non-terminating, non-repeating decimal expansion?

Accepted Answer

√2

Question 2

A hospital records the temperature of a patient every hour. The temperature readings are plotted as points on a graph. Which of the following statements is TRUE about the graph if temperature is a function of time?

Accepted Answer

Each time value corresponds to exactly one temperature value.

Question 3

Which of the following sets is best described by the interval notation (2, 5]?

Accepted Answer

All real numbers x such that 2 \u003c x ≤ 5

Question 4

A function f is defined by f(x) = 1/(x-3). What is the domain of f?

Accepted Answer

All real numbers except x = 3

Question 5

Which of the following is NOT a rational number?

Accepted Answer

π

Question 6

Suppose a chemical reaction's rate is modeled by the function R(t) = 2t + 5, where t is time in seconds. What is the slope of this function, and what does it represent?

Accepted Answer

Slope is 2; it represents the rate of change of the reaction rate per second.

Question 7

Given the sets A = (−∞, 2] and B = [0, ∞), what is A ∩ B?

Accepted Answer

[0, 2]

Question 8

Which of the following best describes the range of the function f(x) = $$x^2$$ for real numbers x?

Accepted Answer

[0, ∞)

Question 9

A student claims that the graph below represents a function. The graph passes through the points (1,2), (1,3), and (2,4). Is the student correct? Why or why not?

Accepted Answer

No, because the graph fails the vertical line test at x = 1.

Question 10

Which of the following is the correct set notation for all real numbers x such that x is greater than or equal to 4 and less than 10?

Accepted Answer

{ x | 4 ≤ x \u003c 10 }

Question 11

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

Accepted Answer

All real numbers t ≥ 0

Question 12

Which of the following statements is TRUE about irrational numbers?

Accepted Answer

They have decimal expansions that neither terminate nor repeat.

Question 13

If f(x) = mx + b is a linear function and f(2) = 7, f(5) = 16, what is the value of m?

Accepted Answer

3

Question 14

Which of the following is the union of the intervals (−∞, 1) and (3, ∞)?

Accepted Answer

(−∞, 1) ∪ (3, ∞)

Question 15

A function g is defined as g(x) = √(x−4). What is the domain of g?

Accepted Answer

All real numbers x ≥ 4

Question 16

Which of the following is an example of a real number that is not rational?

Accepted Answer

π

Question 17

A company tracks the profit P(x) in thousands of dollars as a function of the number of units x sold, given by P(x) = 4x − 20. What is the y-intercept and what does it represent?

Accepted Answer

y-intercept is −20; it represents the profit when no units are sold.

Question 18

Which of the following best describes the set of all integers?

Accepted Answer

All whole numbers, positive and negative, including zero

Question 19

A function h is defined as h(x) = $$1/(x^2$$ − 9). Which values must be excluded from the domain of h?

Accepted Answer

x = 3 and x = −3

Question 20

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

Accepted Answer

A function's graph passes the vertical line test.

MATH 221: First Semester Calculus – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards