Recognize functions from tables | Functions and their graphs | Algebra II | Khan Academy

TL;DR

There is a functional relationship between each person's name and their height in the table and graph provided.

Transcript

We're asked to look at the table below. From the information given, is there a functional relationship between each person and his or her height? So a good place to start is just think about what a functional relationship means. Now, there's definitely a relationship. They say, hey, if you're Joelle, you're 5-6. If you're Nathan, you're 4-11. If yo... Read More

Key Insights

• ❓ A functional relationship means that for every instance of the independent variable, there is only one value of the dependent variable.
• 🧑 In the given table and graph, each person's name corresponds to a unique height value, indicating a functional relationship.
• 🧑 If there were two different height values associated with one person, it would break the functional relationship.
• 🧑 The graph visually represents the functional relationship, with each person's name having one corresponding height value.
• 💄 Ambiguity arises in a function when there are multiple values associated with one input, making it not a valid functional relationship.
• ❓ The concept of functional relationships may seem simple, but it is important in understanding mathematical functions.
• 💄 The graph helps visualize the relationship between names and heights, making it easier to understand the concept of functional relationships.

Questions & Answers

Q: What is a functional relationship?

A functional relationship means that for every instance of the independent variable (in this case, the person's name), there is only one associated value of the dependent variable (height).

Q: How can we determine if the given table and graph represent a functional relationship?

We can determine this by checking if there is only one height value for each person's name. If there were two different heights for one person, it would not be a functional relationship.

Q: Can you explain how the graph shows a functional relationship?

The graph plots the different names on the x-axis and their corresponding heights on the y-axis. Each person's name corresponds to a unique height value, and there are no instances where one person has multiple heights.

Q: What happens if there are two different height values associated with the same person in a table and graph?

If there are two different height values associated with the same person, it would not be a valid functional relationship. The function would be ambiguous, and we wouldn't know which height value to assign to that person.

Summary & Key Takeaways

• A functional relationship means that for each person's name, there must be only one associated height value.

• The table and graph show that each person in the table has a unique height value associated with their name, indicating a functional relationship.

• If there were two different height values associated with one person's name, it would not be considered a functional relationship.