What Are Relations and Functions in Algebra?

TL;DR

Relations in algebra are sets of ordered pairs of input (x) and output (y) values. A relation is a function if each input value has only one corresponding output value; repeating x values with different y values indicate it is not a function. The vertical line test can visually determine if a graph represents a function.

Transcript

in this video we're going to focus on relations and functions so what is a relation a relation is a set of pairs of input and output values here we have three ordered pairs in the first relation on the left the x value is the input value the y value is the output value the x values is associated with the domain of the relation the y values is assoc... Read More

Key Insights

• ❣️ Relations consist of input and output value pairs, where the x values represent the domain and the y values represent the range.
• 🌆 The domain is the set of all x values, while the range is the set of all y values.
• 🪈 In order for a relation to be a function, each input value must have only one corresponding output value.
• ❣️ The presence of repeating x values with different y values indicates that a relation is not a function.
• 📈 The vertical line test can be used to determine if a graph represents a function. If a vertical line intersects the graph at multiple points, the graph does not represent a function.
• ❣️ The domain and range can be determined by listing the x and y values in ascending order.
• ❣️ Checking for repeating x values with different y values is a quick way to identify if a relation is not a function.

Questions & Answers

Q: What is a relation?

A relation is a set of input and output value pairs, with x representing the input and y representing the output.

Q: How do you determine the domain and range of a relation?

To find the domain, list all the x values in ascending order. To find the range, list all the y values in ascending order.

Q: How can you determine if a relation is a function?

A relation is a function if every input value corresponds to only one output value. If an input value corresponds to two or more output values, the relation is not a function.

Q: How can the vertical line test determine if a graph represents a function?

Draw a vertical line on the graph and see if it touches the graph at more than one point. If it does, then the graph does not represent a function.

Summary & Key Takeaways

• Relations are sets of input and output value pairs, where the x value represents the input and the y value represents the output.

• The domain of a relation is the set of x values, and the range is the set of y values.

• In order for a relation to be a function, every input value must have only one output value. Repeating x values with different y values indicate that the relation is not a function.