MCR3U (1.1) - Functions - relations, domain and range

Summary

This video introduces the concept of relations, focusing on independent and dependent variables. It explains how to represent relations in four different ways: tables, coordinate pairs, mapping diagrams, and graphs. Using examples, the video demonstrates how study hours impact test scores and how age affects height. It also defines domain and range, emphasizing the importance of listing values from lowest to highest without repetition. The video concludes with a teaser for the next lesson on functions, which will build upon the examples discussed.

Takeaways

• 🔑 A relation is defined as an ordered pair of values, where X represents the independent variable and Y represents the dependent variable.
• 📚 Two examples of relations discussed are: the impact of study hours on test scores and the effect of age on a person's height.
• 📊 Relations can be displayed in four ways: tables, coordinate form, mapping diagrams, and graphs.
• 📈 In coordinate form, the independent variable is listed first, followed by the dependent variable, as in (2, 55) for 2 hours studied and a score of 55.
• 📝 Mapping diagrams are a way to visually represent relations by listing independent and dependent variables and matching them up.
• 🧩 In mapping diagrams, variables are listed in order from lowest to highest value without repetition, even if they appear more than once in the data.
• 📉 Graphs are used to plot the points from the relations, with the independent variable on the x-axis and the dependent variable on the y-axis.
• 📌 The domain of a relation is the set of all possible values of the independent variable, listed from lowest to highest without repetition.
• 🌟 The range of a relation is the set of all possible values of the dependent variable, also listed from lowest to highest without repetition.
• 📚 The concepts of domain and range will be further explored in future videos, with a focus on understanding functions.

Q & A

What is a relation in the context of mathematics?

A relation is an ordered pair of X values (independent variable) and Y values (dependent variable). The X values represent the independent variable, and the Y values represent the dependent variable.

In the first example, what is the independent and dependent variable?

In the first example, the number of hours studied is the independent variable, and the final mark on the test is the dependent variable.

How can relations be represented?

Relations can be represented in four ways: a table of values, a list of coordinates, a mapping diagram, and a graph.

What is a mapping diagram and how is it used?

A mapping diagram is a visual representation where the independent and dependent variables are listed in boxes, and lines are drawn to connect related values. Variables are listed in order, and each variable appears only once.

How do you represent a relation in a graph?

In a graph, the independent variable is plotted on the x-axis, and the dependent variable is plotted on the y-axis. Points are plotted based on the coordinate pairs derived from the table of values.

What is the domain of a relation?

The domain is the set of all values of the independent variable in a relation, listed from lowest to highest, without repetition.

What is the range of a relation?

The range is the set of all values of the dependent variable in a relation, listed from lowest to highest, without repetition.

Why is it important to list variables in order in mapping diagrams?

Listing variables in order (from lowest to highest) helps maintain clarity and organization in the representation of relationships between variables, ensuring accuracy.

How does domain and range relate to mapping diagrams?

Both domain and range are similar to mapping diagrams, as they list the values of the independent (domain) and dependent (range) variables in order without repeating any value.

What concept will be covered in the next video following this one?

The next video will cover the concept of functions, which is an important mathematical concept related to relations and will be tested in the course.