Identifying Functions from Relations

What is the primary condition for a relation to be considered a function?

• All x-values must be positive.

• Each y-value must be unique.

• Each x-value must correspond to exactly one y-value.

• The function must pass the vertical line test.

In the provided table, why was the relation considered a function?

• Because no x-values were repeating.

• Because it contained only positive numbers.

• Because all y-values were unique.

• Because it had repeating x-values.

How can you determine if a relation is a function by looking at a table?

• Ensure the table has at least three columns.

• Ensure all values are integers.

• Check if the y-values repeat.

• Check if the x-values do not repeat.

Why is it important for each x-value to correspond to exactly one y-value in a function?

• To ensure all x-values are used.

• To make the function easier to graph.

• To satisfy the definition of a function.

• To ensure the function is linear.

If an x-value in a table appears more than once with different y-values, what does this imply?

• The relation becomes a linear function.

• The relation is not a function.

• The relation is still a function.

• The relation is only a function if it passes the horizontal line test.

What would happen if an x-value in the relation had multiple corresponding y-values?

• It would still be considered a function.

• It would not affect the function status.

• It would mean the relation is not a function.

• It would turn the relation into a quadratic function.

What change to the table would make the relation not a function?

• Adding more rows with unique x-values.

• Replacing some x-values to make them repeat with different y-values.

• Making all y-values the same.

• Converting all numerical values to their absolute values.

What does it mean if an x-value has two different y-values in a relation?

• The relation is a function.

• The relation is not a function.

• The relation is a multi-function.

• The relation is a complex function.

If a table is modified and an x-value now repeats with different y-values, what is the impact?

• The table must be discarded as invalid.

• The table becomes a perfect function.

• The table no longer represents a function.

• The table becomes more complex but remains a function.