Question 1

Which of the following sets contains all real numbers x such that x2 ?

Accepted Answer

{x | -2

Question 2

Which of the following numbers is NOT a rational number?

Accepted Answer

\sqrt{2}

Question 3

Suppose you are given the function f(x) = \frac{1}{x-2}. What is the domain of f?

Accepted Answer

{x \in \mathbb{R} | x 
eq 2}

Question 4

Which of the following statements about the set of real numbers \mathbb{R} is TRUE?

Accepted Answer

Every real number can be represented as an infinite decimal expansion.

Question 5

Given the function f(x) = 3x + 5, what is the slope of its graph?

Accepted Answer

3

Question 6

Which of the following is the correct interval notation for the set {x | 1 \leq x ?

Accepted Answer

[1,4)

Question 7

A function f is defined by f(x) = $$x^2 - 4x + 3. $$What is the range of f?

Accepted Answer

{y | y \geq -1}

Question 8

Which of the following best describes a function?

Accepted Answer

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

Question 9

If f(x) = \sqrt{x-1}, what is the domain of f?

Accepted Answer

{x \in \mathbb{R} | x \geq 1}

Question 10

Which of the following is an example of a piecewise defined function?

Accepted Answer

f(x) = \begin{cases} $$x^2$$ & x

Question 11

Suppose you are modeling the distance (in meters) a car travels as a function of time (in seconds) with d(t) = 20t + 5. What does the number 20 represent in this context?

Accepted Answer

The speed of the car in meters per second.

Question 12

Which of the following is the correct set notation for the set of all real numbers except 3?

Accepted Answer

\mathbb{R} \setminus \{3\}

Question 13

If f(x) = 2x + 1 and g(x) = $$x^2$$, what is (f \circ g)(2)?

Accepted Answer

9

Question 14

Which of the following is the correct definition of the distance between two real numbers a and b?

Accepted Answer

|a-b|

Question 15

A function f is defined on \mathbb{R} by f(x) = \frac{1}{$$x^2$$}. What is the domain of f?

Accepted Answer

{x \in \mathbb{R} | x 
eq 0}

Question 16

Which of the following is a correct graphical interpretation of the solution to $$x^2 = 2$$?

Accepted Answer

The x-coordinates where the graph of y = $$x^2$$ intersects the line y = 2.

Question 17

Which of the following is the correct set notation for the interval containing all real numbers greater than or equal to 0 and less than 5?

Accepted Answer

[0,5)

Question 18

If f(x) = $$x^2$$ and g(x) = x+1, what is f(g(2))?

Accepted Answer

9

Question 19

Which of the following is NOT a function?

Accepted Answer

A rule that assigns to some x in the domain more than one y in the range.

MATH 221: First Semester Calculus – Numbers, Functions, and Foundations

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