Identifying Functions Through Relations and Graphs

The video tutorial explains the concept of functions as a special type of relation, emphasizing that each x-value must be associated with only one y-value. It provides examples to distinguish between functions and non-functions, introduces the vertical line test for graphical identification, and explains how to determine if an equation represents a function by examining the exponent of y.

What makes a function a special type of relation?

• Each y-value can be associated with multiple x-values.

• Each y-value must be associated with only one x-value.

• Each x-value must be associated with only one y-value.

• Each x-value can be associated with multiple y-values.

In the given example, why is set A not considered a function?

• Because it has more y-values than x-values.

• Because it has more x-values than y-values.

• Because it has repeating x-values.

• Because it has repeating y-values.

Why is set B considered a function?

• Because it has no repeating x-values.

• Because it has more y-values than x-values.

• Because it has repeating y-values.

• Because it has more x-values than y-values.

What must be true for a set of ordered pairs to be considered a function?

• It must have repeating x-values.

• It must have no repeating y-values.

• It must have no repeating x-values.

• It must have more y-values than x-values.

In the table of values example, why is the set not considered a function?

• Because it has no repeating x-values.

• Because it has repeating x-values.

• Because it has more y-values than x-values.

• Because it has repeating y-values.

What does the vertical line test help determine?

• If a graph has repeating x-values.

• If a graph has more y-values than x-values.

• If a graph has repeating y-values.

• If a graph represents a function.

What happens if a vertical line intersects a graph at more than one point?

• The graph has no repeating x-values.

• The graph represents a function.

• The graph does not represent a function.

• The graph has repeating y-values.

How can you identify a function from an equation without solving for y?

• By looking at the exponent of x.

• By looking at the exponent of y.

• By checking if the equation has repeating y-values.

• By checking if the equation has repeating x-values.

Which exponent of y indicates that an equation is a function?

• An odd number.

• An even number.

• A negative number.

• A positive number.

In the equation y = x^2 + 3, why is it considered a function?

• Because the exponent of x is an even number.

• Because the exponent of x is an odd number.

• Because the exponent of y is an even number.

• Because the exponent of y is an odd number.