Determining Functions: Relations and Their Types

The video tutorial explores the concept of functions in algebra, focusing on how to determine if a relation is a function. It covers various representations, including tables, mapping diagrams, ordered pairs, and graphs. The tutorial explains that a relation is a function if each input has exactly one output. It provides specific methods for each representation, such as checking for repeated x-values in tables and ordered pairs, ensuring single arrows in mapping diagrams, and using the vertical line test for graphs. The video concludes with a recap of these methods.

What is the key question being asked in most algebra classes?

• Is a number even?

• Is a relation a function?

• Is a shape symmetrical?

• Is a sequence arithmetic?

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What must be true for a relation to be considered a function?

• Every input has exactly one output.

• All values are integers.

• There are no negative values.

• Every output has exactly one input.

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How can you determine if a table represents a function?

• Check if there are any repeated x values.

• Check if there are any repeated y values.

• Check if the table has an even number of rows.

• Check if all values are positive.

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In a table, what does it mean if there are no repeated x values?

• The table has an error.

• The table is incomplete.

• The table does not represent a function.

• The table represents a function.

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In a mapping diagram, what indicates that the relation is not a function?

• An input has more than one arrow coming from it.

• An output has more than one arrow coming to it.

• There are more outputs than inputs.

• There are more inputs than outputs.

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In a mapping diagram, what does it mean if each input has only one arrow coming from it?

• The diagram is incomplete.

• The diagram represents a function.

• The diagram does not represent a function.

• The diagram has an error.

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What should you look for in ordered pairs to determine if they represent a function?

• Repeated y values.

• Positive values.

• Repeated x values.

• Negative values.

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In ordered pairs, what does it mean if an x value is repeated?

• The ordered pairs are incomplete.

• The ordered pairs do not represent a function.

• The ordered pairs represent a function.

• The ordered pairs have an error.

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What test is used to determine if a graph represents a function?

• Horizontal line test.

• Diagonal line test.

• Vertical line test.

• Curved line test.

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What does it mean if a vertical line passes through a graph more than once?

• The graph represents a function.

• The graph does not represent a function.

• The graph is symmetrical.

• The graph is linear.

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