Question 1

Which of the following numbers is irrational?

Accepted Answer

π

Question 2

A hospital monitors the temperature of a patient every hour. If the temperature at hour t is given by T(t) = 37 + 0.5t, what is the domain of this function if the patient is monitored for 8 hours?

Accepted Answer

[0, 8]

Question 3

Which of the following sets describes all real numbers x such that x is greater than 2 and less than or equal to 5?

Accepted Answer

(2, 5]

Question 4

A function f is defined by f(x) = 1/(x-3). What is the largest possible domain of f in set-builder notation?

Accepted Answer

{ x | x ≠ 3 }

Question 5

Which of the following graphs would fail the vertical line test?

Accepted Answer

A circle defined by $$x^2$$ + $$y^2 = 1$$

Question 6

If the distance between two points on the number line is 7 and one point is at x = 3, what are the possible values for the other point?

Accepted Answer

x = 10 or x = -4

Question 7

Which of the following statements about real numbers is TRUE?

Accepted Answer

Every real number can be represented as a point on the number line.

Question 8

Given the function f(x) = √(x−2), what is the domain of f?

Accepted Answer

[2, ∞)

Question 9

A company’s profit P as a function of units sold x is given by P(x) = 5x − 200. What is the y-intercept of this function, and what does it represent?

Accepted Answer

−200; the initial loss before any units are sold

Question 10

Which of the following is NOT a function?

Accepted Answer

A relation where each input has two different outputs

Question 11

If A = { x | 0 \u003c x \u003c 4 } and B = { x | $$x^2$$ \u003c 9 }, what is A ∩ B?

Accepted Answer

{ x | 0 \u003c x \u003c 3 }

Question 12

Which of the following best describes the range of the function f(x) = $$x^2$$ for x in the interval [−2, 3]?

Accepted Answer

[0, 9]

Question 13

A medication’s concentration in the bloodstream is modeled by C(t) = 10 − t for t in [0, 10]. What is the range of C?

Accepted Answer

[0, 10]

Question 14

Which of the following is the correct interval notation for all real numbers except 2?

Accepted Answer

(−∞, 2) ∪ (2, ∞)

Question 15

Which of the following statements about the function f(x) = 1/x is correct?

Accepted Answer

The function is undefined at x = 0.

Question 16

A car travels at a constant speed of 60 km/h. Which function models the distance d (in km) from the starting point after t hours?

Accepted Answer

d(t) = 60t

Question 17

Which of the following is a rational number?

Accepted Answer

0.333... (repeating decimal)

Question 18

If f(x) = mx + b is a linear function with m = −3 and b = 5, what is the slope and y-intercept of the line?

Accepted Answer

Slope: −3, y-intercept: 5

Question 19

Which of the following best describes the set { x | $$x^2$$ \u003c 4 } in interval notation?

Accepted Answer

(−2, 2)

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

Study Guide - Practice Questions

Study Guide - Flashcards