Understanding Functions and Their Components

The video introduces functions, explaining them as rules that assign specific outputs to inputs. It uses examples like prepaid cell phone costs and cable bills to illustrate function notation, domain, and range. The video also covers independent and dependent variables, and provides examples to determine domain and range, such as taxi fares and theme park rides.

What is a function in mathematical terms?

• A machine that produces random outputs

• A process that does not involve inputs

• A rule that assigns a specific output for every input

• A rule that assigns multiple outputs for each input

In the prepaid cell phone example, what is the output if the input is 200 minutes?

• $45

• $15

• $60

• $30

What does function notation replace in traditional equations?

• The variable X

• The variable Y

• The multiplication sign

• The equal sign

In the cable bill example, what is the fixed cost component?

• $10 per movie

• $3 per movie

• $70 monthly fee

• $50 monthly fee

What is the domain of a function?

• The set of all possible outputs

• The set of all possible inputs

• The set of all possible variables

• The set of all possible equations

In the taxi fare example, what is the minimum cost if no miles are traveled?

• $7

• $3

• $0

• $4

What is the range of a function?

• The set of all possible inputs

• The set of all possible equations

• The set of all possible variables

• The set of all possible outputs

In the theme park example, what is the cost for 3 rides?

• $5

• $7

• $11

• $9

How is the domain expressed in the theme park example?

• All positive integers

• All negative integers

• All non-negative integers

• All even numbers

What pattern does the range follow in the theme park example?

• Composite numbers

• Even numbers

• Odd numbers

• Prime numbers