Question 1

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

Accepted Answer

√2

Question 2

A hospital monitors the temperature of a patient every hour. The temperature, T, as a function of time, t (in hours), is recorded. Which of the following best describes this relationship?

Accepted Answer

T is a function of t because each time t has exactly one temperature T.

Question 3

Which of the following intervals represents all real numbers greater than or equal to -3 and less than 5?

Accepted Answer

[-3, 5)

Question 4

A function f is defined as f(x) = $$x^2$$ for x ≤ 0 and f(x) = x for x \u003e 0. What is the value of f(-2) + f(3)?

Accepted Answer

7

Question 5

Which of the following statements is TRUE about the number π (pi)?

Accepted Answer

It is an irrational number because its decimal expansion is non-terminating and non-repeating.

Question 6

A company models its profit P as a function of the number of units sold, x, by P(x) = 20x - 100. What is the y-intercept of this function, and what does it represent?

Accepted Answer

y-intercept is -100; it represents the initial loss before any units are sold.

Question 7

Which of the following sets is described by the set-builder notation { x | 2 \u003c x ≤ 7 }?

Accepted Answer

(2, 7]

Question 8

If A = [1, 5] and B = (3, 7], what is A ∩ B (the intersection of A and B)?

Accepted Answer

(3, 5]

Question 9

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

Accepted Answer

A parabola opening upwards

Question 10

The function f(x) = √x is defined for which set of real numbers?

Accepted Answer

x ≥ 0

Question 11

A scientist records the pH of a solution as a function of time. If the pH at time t is given by pH(t) = 7 - 0.5t for t in [0, 10], what is the range of the function?

Accepted Answer

[2, 7]

Question 12

Which of the following is NOT a rational number?

Accepted Answer

√2

Question 13

If the distance between two points a and b on the real number line is 8, and a = 3, what are the possible values for b?

Accepted Answer

b = 11 or b = -5

Question 14

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

Accepted Answer

[0, 9]

Question 15

A piecewise function is defined as f(x) = { 2x+1 if x \u003c 0; $$x^2 if x$$ ≥ 0 }. What is f(-3) + f(2)?

Accepted Answer

5

Question 16

Which of the following statements about the real number line is correct?

Accepted Answer

Every point on the real number line corresponds to a real number.

Question 17

If f(x) = 3x - 2, what is the slope of the function and what does it represent in a real-world context (e.g., cost per item)?

Accepted Answer

Slope is 3; it represents the rate of change per unit increase in x.

Question 18

Which of the following is the union of the intervals (1, 4) and [3, 6]?

Accepted Answer

(1, 6]

Question 19

A function g is defined on the domain [0, 5). Which of the following values is NOT in the domain of g?

Accepted Answer

5

Question 20

Which of the following best describes a function in the context of calculus?

Accepted Answer

A rule that assigns to each element in the domain exactly one element in the range.

MATH 221: First Semester Calculus – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards