Understanding Function Notation and Waste Statistics

The video tutorial introduces function notation using waste generation statistics from 2008. It explains how the amount of waste produced by a city is a function of its population, using Flagstaff, Arizona as an example. The tutorial clarifies the concepts of independent and dependent variables, emphasizing that population is the input and waste is the output. It concludes with a review of the definition of a function, highlighting the unique relationship between inputs and outputs.

In 2008, what percentage of waste was recycled in the United States?

• 24.3%

• 4.5%

• 8.9%

• 66.8%

What is the relationship between waste produced and population in the given example?

• Waste and population are unrelated

• Population is a function of waste

• Waste is a function of population

• Waste is independent of population

If a city has a population of 65,000, how should it be represented in the function notation?

• F(273)

• F(65,000)

• F(65)

• F(273,000)

In the example, what is the output when the population input is 65?

• 65,000 pounds

• 65 pounds

• 273,000 pounds

• 273 pounds

What is the independent variable in the function relating population and waste?

• Waste

• Population

• Time

• Location

Which statement is true about the relationship between population and waste?

• They are independent of each other

• Population controls the waste

• Waste controls the population

• Both are dependent variables

Which of the following best describes a dependent variable?

• It is controlled by the independent variable

• It controls the independent variable

• It is always constant

• It is unrelated to the independent variable

What is a function in mathematical terms?

• A rule that relates multiple inputs to one output

• A rule that relates one input to multiple outputs

• A rule that relates each input to exactly one output

• A rule that relates outputs to inputs

In function notation, if Y = F(X), what does Y represent?

• Y is the input

• Y is the function

• Y is the independent variable

• Y is the output

What does it mean when we say 'Y is a function of X'?

• Y and X are the same

• Y determines X

• X determines Y

• Y and X are unrelated