Question 1

Which of the following sets contains all real numbers x such that 1 \u003c x \u003c 6?

Accepted Answer

C = { x | 1 \u003c x \u003c 6 }

Question 2

Which of the following fractions has a finite decimal expansion?

Accepted Answer

38

Question 3

Given the function f(x) = x, what is its domain?

Accepted Answer

All real numbers x 	ext{ such that } x 	ext{ is nonnegative}

Question 4

If f(x) = mx + b is a linear function, what does the parameter m represent?

Accepted Answer

The slope of the line

Question 5

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

Accepted Answer

|a - b|

Question 6

Suppose you are given the function f(x) = 1x. What is the domain of f?

Accepted Answer

All real numbers except x = 0

Question 7

Which of the following statements about the graph of a function is TRUE?

Accepted Answer

The graph of a function consists of all pairs (x, f(x)) where x is in the domain.

Question 8

Which property must a set satisfy to be considered an interval on the real number line?

Accepted Answer

It must contain all real numbers between any two of its elements.

Question 9

If f(x) = $$x^2$$, what is the range of f?

Accepted Answer

All real numbers y 	ext{ such that } y 	ext{ is nonnegative}

Question 10

Which of the following is NOT a characteristic of a function?

Accepted Answer

Each output can have multiple corresponding inputs.

Question 11

Consider the set D = 	ext{solutions to } $$x^2 - x - 1 = 0. $$How many elements does D have?

Accepted Answer

Two

Question 12

Which of the following is the correct interval notation for all real numbers x such that 2 	ext{ ≤ } x 	ext{ ?

Accepted Answer

[2, 5)

Question 13

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

Accepted Answer

f(x) = {$$x^2x 	$$ext{ if } x 	ext{ ≥ } 0-xx 	ext{ if } x 	ext{

Question 14

If the graph of a relation fails the vertical line test, what does this indicate?

Accepted Answer

The relation is not a function.

Question 15

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

Accepted Answer

Q = 	ext{set of all rational numbers}

Question 16

Which of the following is a real-world example of a function?

Accepted Answer

The relationship between the temperature and the time of day

Question 17

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

Accepted Answer

9

Question 18

Which of the following is the correct definition of a function?

Accepted Answer

A relation where each input has exactly one output

Question 19

If f(x) = 2x + 3, what is the value of f(-1)?

Accepted Answer

1

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

Study Guide - Practice Questions