What is the Difference Between Discrete Function and Continuous Function?

The main difference between discrete and continuous functions lies in the values they can take and the way they are represented graphically. Here are the key differences:

• Discrete Functions:
• Have distinct and separate values with no values in between the points already given.
• Can only take certain points in the interval, usually integers or whole numbers.
• Represented by scatter plots with scattered points.
• Examples include the number of televisions or the number of puppies born.
• Continuous Functions:
• Can take on any number within a certain interval.
• Connect all their values, with no noticeable gaps in their graphs.
• Represented by lines or curves, including straight lines in the case of linear functions.
• Can be any value within a certain interval, such as the continuous function y = 3x.

In summary, discrete functions have distinct and separate values with no values in between, while continuous functions can take on any number within a certain interval and connect all their values. Discrete functions are represented by scatter plots, whereas continuous functions are represented by lines or curves.

Comparative Table: Discrete Function vs Continuous Function

The main difference between discrete and continuous functions lies in the values they can take and how they are represented graphically. Here is a table summarizing the differences between discrete and continuous functions:

Discrete functions are used to represent things that can be counted and have noticeable points and gaps in their graphs. Continuous functions, on the other hand, connect all the dots and can take any value within a certain interval, making their graphs appear as lines or curves.