Discrete vs. Continuous Functions Explained

The video tutorial explains the differences between discrete and continuous functions. Discrete functions have specific, separate values, often represented by isolated points on a graph. Examples include counting students or tickets, where only whole numbers are possible. Continuous functions, on the other hand, can take any value within a range, represented by an unbroken line on a graph. Examples include measuring height or time, where values can be fractions or decimals. The video also covers how to identify these functions on graphs, noting that continuous graphs can be drawn without lifting the pen, while discrete graphs consist of distinct points.

What is a key characteristic of a discrete function?

• It always includes decimal numbers.

• It can only take certain values.

• It is represented by a continuous line.

• It can take any value.

Why can't the number of students in a class be a decimal?

• Because it is a continuous function.

• Because decimals are not allowed in counting.

• Because students can only be counted in whole numbers.

• Because it is a negative number.

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

• Calories consumed

• Height of students

• Number of stories in a building

• Distance run over time

What is a key characteristic of a continuous function?

• It can only take whole numbers.

• It is represented by isolated points.

• It can take any value, including decimals.

• It always has a start and stop.

How can you identify a continuous graph?

• It has gaps and jumps.

• It has isolated points.

• It only includes whole numbers.

• It can be drawn without lifting the pen.

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

• Number of tickets sold

• Height of students

• Number of stories in a building

• Number of students in a class

Why can the number of calories consumed be considered a continuous function?

• Because it is always a positive number.

• Because it can only be whole numbers.

• Because it is always a negative number.

• Because it can include decimal values.

What makes a graph not continuous?

• It has a hole.

• It is a solid line.

• It can be drawn without lifting the pen.

• It includes decimal values.

What happens if a graph has a jump?

• It is considered discrete.

• It is considered continuous.

• It is a solid line.

• It can take any value.

What should you remember about continuous graphs?

• They only include whole numbers.

• They can be drawn without lifting the pen.

• They can have isolated points.

• They always go on infinitely.