Table of contents

0. Functions4h 53m
1. Limits and Continuity2h 2m
2. Intro to Derivatives1h 33m
3. Techniques of Differentiation2h 18m
4. Derivatives of Exponential & Logarithmic Functions1h 16m
- Derivatives of Exponential & Logarithmic Functions
  1h 16m
5. Applications of Derivatives2h 19m
6. Graphical Applications of Derivatives6h 0m
7. Antiderivatives & Indefinite Integrals48m
- Antiderivatives
  17m
- Indefinite Integrals
  31m
8. Definite Integrals4h 36m
9. Graphical Applications of Integrals1h 43m
- Area Between Curves
  1h 19m
- Introduction to Volume & Disk Method
  23m
10. Integrals of Inverse, Exponential, & Logarithmic Functions21m
- Integrals of Exponential Functions
  14m
- Integrals Involving Logarithmic Functions
  7m
11. Techniques of Integration2h 7m
- Integration by Parts
  1h 37m
- Improper Integrals
  29m
12. Trigonometric Functions6h 54m
13: Intro to Differential Equations2h 23m
14. Sequences & Series2h 8m
15. Power Series2h 19m
- Power Series & Taylor Series
  2h 19m
16. Probability & Calculus45m
- Continuous Probability Models
  45m

0. Functions

Introduction to Functions

Business Calculus

0. Functions

Introduction to Functions

Previous problemNext problem

Struggling with Business Calculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

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

A table that lists all possible input and output pairs without any specific rule.

A relationship that assigns exactly one output value to each input value from a given set.

A calculation that only uses constant values and does not depend on any input.

A process that randomly matches inputs to multiple outputs.

Previous problemNext problem

Verified step by step guidance

Step 1: Understand the definition of a function in the context of calculus. A function is a relationship where each input (from the domain) is assigned exactly one output (from the range). This is a key concept in calculus and is foundational for understanding how variables interact in mathematical models.

Step 2: Analyze the options provided in the problem. Eliminate any options that do not align with the definition of a function. For example, a table listing all possible input-output pairs without a specific rule does not meet the criteria of a function because it lacks a defined relationship.

Step 3: Consider the option that describes a calculation using only constant values. This does not depend on any input and therefore does not represent a function, as a function requires a relationship between inputs and outputs.

Step 4: Evaluate the option describing a process that randomly matches inputs to multiple outputs. This violates the definition of a function, as a function must assign exactly one output to each input.

Step 5: Conclude that the correct answer is the option stating 'A relationship that assigns exactly one output value to each input value from a given set,' as this aligns with the formal definition of a function in calculus.