Overview of functions - Online Math - What are functions

The video tutorial provides an overview of functions, explaining them as relationships between two sets. It covers the concept of input and output, unique mapping rules, and naming conventions for functions. The tutorial also discusses the domain and range of functions, including the concept of implied domain, and highlights situations where a function relationship may not exist.

What is a function in terms of sets?

• A collection of unrelated elements

• A relationship between two sets where each input has a unique output

• A set of numbers only

• A random mapping of elements

Which of the following scenarios would NOT be considered a valid function relationship?

• Multiple inputs map to the same output

• An input maps to two different outputs

• All inputs are mapped to outputs

• Every input has a unique output

What does F(x) represent in function notation?

• The domain of the function

• The output value of the function at x

• The input value of the function

• The name of the function

How do you evaluate a function at a specific numeric value?

• By adding the numeric value to the function

• By substituting the numeric value for x in the function

• By dividing the function by the numeric value

• By multiplying the numeric value with the function

What is the domain of a function?

• The set of all possible input values

• The set of all numbers

• The set of all letters

• The set of all possible output values

Which of the following is NOT a limitation of the implied domain?

• Having a zero in the denominator

• Multiplying by zero

• Taking the square root of a negative number

• Dividing by zero

What is the range of a function?

• The set of all numbers

• The set of all possible output values

• The set of all possible input values

• The set of all letters