Question 1

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

Accepted Answer

π

Question 2

A patient’s body temperature, T (in °C), is modeled by the function T(t) = 37 + 0.5 sin(πt/12), where t is hours after midnight. What is the domain of this function if t represents time over a 24-hour day?

Accepted Answer

[0, 24]

Question 3

Which of the following sets is best described by the set-builder notation {x | 2 \u003c x ≤ 5}?

Accepted Answer

The half-open interval (2, 5]

Question 4

Suppose 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

A chemical reaction’s rate R (in mol/s) is given by R(c) = √(c-1), where c is the concentration in mol/L. For which values of c is this function defined?

Accepted Answer

c ≥ 1

Question 6

Which of the following statements is TRUE about the number -√2?

Accepted Answer

It is an irrational number

Question 7

If A = {x | x ≥ 0} and B = {x | x \u003c 5}, what is A ∩ B?

Accepted Answer

{x | 0 ≤ x \u003c 5}

Question 8

A function g is defined by g(x) = $$x^2 + 1. $$Which of the following is the range of g?

Accepted Answer

[1, ∞)

Question 9

Which of the following graphs passes the vertical line test and thus represents a function?

Accepted Answer

A parabola opening upwards

Question 10

A taxi company charges a flat fee of $$3 plus 2 $$per mile. Which function models the total cost C (in dollars) for a ride of m miles?

Accepted Answer

C(m) = 2m + 3

Question 11

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

Accepted Answer

They can be non-terminating and non-repeating decimals

Question 12

If the distance between two points a and b on the real number line is 7, which equation must be true?

Accepted Answer

|a - b| = 7

Question 13

Which of the following is the correct set notation for the union of the intervals (−∞, 2) and (1, ∞)?

Accepted Answer

(−∞, 2) ∪ (1, ∞)

Question 14

A function h is defined by h(x) = $$1/(x^2 - 4). $$What is the domain of h?

Accepted Answer

All real numbers except x = 2 and x = -2

Question 15

Which of the following statements is TRUE?

Accepted Answer

All rational numbers are real

Question 16

A function models the height h (in meters) of a ball thrown upward as h(t) = $$-4.9t^2 + 20t + 1. $$What is the domain of this function in the context of the ball’s flight?

Accepted Answer

0 ≤ t ≤ T, where T is when h(T) = 0

Question 17

Which of the following is the correct interval notation for the set {x | x ≥ -3 and x \u003c 7}?

Accepted Answer

[-3, 7)

Question 18

If f(x) = √(5 - x), what is the range of f?

Accepted Answer

[0, √5]

Question 19

Which of the following is NOT a function?

Accepted Answer

The relation x = $$y^2$$

Question 20

A medical dosage is given by D(w) = 0.1w + 5, where w is the patient’s weight in kg. If a patient weighs 70 kg, what is the correct dosage?

Accepted Answer

12 units

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

Study Guide - Practice Questions

Study Guide - Flashcards