Understanding Discrete and Continuous Graphs

This lesson explains the difference between discrete and continuous variables in equations by examining their solutions on graphs. It uses examples of Josie's DVD purchases to illustrate discrete graphs and Brian's game time to demonstrate continuous graphs. Discrete graphs have isolated points, while continuous graphs have connected points. The lesson emphasizes understanding when to connect points based on the context of the problem.

What is a common misunderstanding about solutions plotted on graphs?

• They must always be whole numbers.

• They must always be positive.

• They must always be connected.

• They must always be integers.

Why are the points on Josie's DVD graph not connected?

• Because the cost of DVDs is not fixed.

• Because Josie can buy fractional DVDs.

• Because Josie can buy an unlimited number of DVDs.

• Because Josie cannot buy partial DVDs.

What type of graph is used to represent Josie's DVD purchases?

• Logarithmic graph

• Exponential graph

• Discrete graph

• Continuous graph

Why are the points on Brian's game graph connected?

• Because Brian pays for portions of minutes.

• Because Brian pays for whole minutes only.

• Because the game charges a flat rate.

• Because Brian plays for a fixed number of minutes.

What does a continuous graph indicate about the solutions?

• They are only whole numbers.

• They are only integers.

• They can be both integers and fractions.

• They are only positive numbers.