Discrete and Continuous Functions

This video tutorial covers discrete and continuous functions, explaining their differences and characteristics. Discrete functions have input values that are counted, often represented by integers, and their graphs resemble scatter plots. Continuous functions allow input values to be measured, with graphs that are connected lines or curves. The video provides examples of both types of functions, including real-world scenarios like the height of a ball and the cost of food at a wedding. It also includes problem-solving exercises involving gasoline costs and hotel room reservations, demonstrating how to model these situations with equations and graphs.

What is a key characteristic of a discrete function?

• Input values can be any real number.

• Input values are counted and often integers.

• The graph is a smooth curve.

• The graph is always a straight line.

How can you describe a continuous function?

• It only includes whole numbers.

• It is represented by isolated points.

• It has gaps between points.

• Its graph can be drawn without lifting the pencil.

Which of the following is an example of a continuous function?

• Number of books in a library.

• Height of a ball thrown in the air.

• Number of students in a class.

• Cost of apples per dozen.

What is the input quantity for the braking distance of a cement truck?

• Weight in tons

• Speed in miles per hour

• Time in seconds

• Distance in feet

Which example represents a discrete function?

• Height of a plant over time

• Temperature change throughout the day

• Number of oranges in a bag

• Speed of a car over time

Why is the number of rooms reserved for a trip considered a discrete function?

• Rooms can be reserved in fractions.

• Rooms can only be reserved in whole numbers.

• The cost per room varies.

• The stay duration is flexible.

What is the equation for the cost of gasoline if it costs $2.50 per gallon?

• c = 2.50g

• c = 2.50 + g

• c = 2.50 - g

• c = g/2.50

In the hotel room reservation example, what is the cost for reserving 5 rooms for two nights?

• $2,100

• $1,800

• $1,500

• $1,200

What pattern is observed in the cost of gasoline as the number of gallons increases?

• The cost decreases by $5.

• The cost doubles for every gallon.

• The cost remains constant.

• The cost increases by $5 for every 2 gallons.

How is the graph of a discrete function represented?

• As a continuous line

• As a set of connected points

• As a smooth curve

• As a set of isolated points