Question 1

Which of the following numbers is irrational?

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 hour 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

The decimal expansion of 0.121212... (where '12' repeats forever) is:

Accepted Answer

Infinite and rational

Question 5

Which set contains all rational numbers?

Accepted Answer

ℚ

Question 6

A function is defined by f(x) = 1/(x-3). What is the biggest possible domain for this function?

Accepted Answer

All real numbers except x = 3

Question 7

Which of the following graphs could NOT represent a function?

Accepted Answer

A circle centered at the origin

Question 8

If the distance between two points a and b on the real line is 7, which of the following could be true?

Accepted Answer

|a - b| = 7

Question 9

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

Accepted Answer

Question 10

Which of the following is the correct set notation for all real numbers x such that x is less than 4?

Accepted Answer

{x | x \u003c 4}

Question 11

A chemist measures the concentration of a solution as a function of time. If the concentration at time t is given by C(t) = 5 - $$t^2$$, what is the range of C(t) for t in [0, 2]?

Accepted Answer

[1, 5]

Question 12

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

Accepted Answer

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

Question 13

Which of the following is NOT a linear function?

Accepted Answer

f(x) = $$x^2 + 1$$

Question 14

A function f is defined on the domain x \u003e 0 by f(x) = 1/√x. Which of the following is NOT in the range of f?

Accepted Answer

0

Question 15

Which of the following best explains why the diagonal of a unit square is irrational?

Accepted Answer

Because its length is √2, which cannot be written as a fraction of two integers.

Question 16

A student claims that the graph of $$y^2 = x is a $$function. Using the vertical line test, what is the correct evaluation?

Accepted Answer

It is not a function, because some vertical lines cross the graph more than once.

Question 17

Which of the following numbers has a finite decimal expansion?

Accepted Answer

1/4

Question 18

If a function f assigns to each x in its domain exactly one output f(x), which of the following situations violates the definition of a function?

Accepted Answer

A machine that gives two different outputs for the same input.

Question 19

Which of the following is the correct set notation for the open interval between -1 and 3?

Accepted Answer

(-1, 3)

Question 20

A real-world example: The cost C(q) of producing q units of a product is given by C(q) = 100 + 5q. What is the slope of this linear function, and what does it represent?

Accepted Answer

5; it represents the cost per additional unit produced.

MATH 221: First Semester Calculus – Study Notes

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