Understanding Functions from Tables

The video tutorial explains how to determine if a table represents a function by analyzing the relationship between x and y values. A function is defined as a relation where each input (x value) has exactly one output (y value). The tutorial examines four tables, identifying which ones are functions based on whether any x value has more than one corresponding y value. The first and fourth tables are not functions due to multiple outputs for a single input, while the second and third tables are functions as each input has a unique output.

What is a key characteristic of a function in terms of x and y values?

• Each x value can have multiple y values.

• Each x value has exactly one y value.

• Each y value has exactly one x value.

• Each y value can have multiple x values.

Why is the first table not considered a function?

• It has more y values than x values.

• It has repeated x values with different y values.

• It has repeated y values with different x values.

• It has no y values.

What does mapping a relation help to visualize?

• The number of y values.

• The relationship between domain and range.

• The total number of values.

• The number of x values.

What makes the second table a function?

• Each x value has exactly one y value.

• Each y value has exactly one x value.

• Each y value has multiple x values.

• Each x value has multiple y values.

Is it acceptable for different x values to share the same y value in a function?

• No, because it violates the definition of a function.

• No, each x value must have a unique y value.

• Yes, but only if the y values are positive.

• Yes, as long as each x value has one y value.

What is the domain of the second table?

• Negative one, three, five, eight, and sixteen.

• One, three, five, and seven.

• Zero, one, nine, and fourteen.

• Negative four, two, five, seven, and fifteen.

Why is the third table considered a function?

• It has repeated x values.

• It has unique x values.

• It has no y values.

• It has repeated y values.

What is the issue with the fourth table that makes it not a function?

• It has unique x values.

• It has repeated y values.

• It has repeated x values with different y values.

• It has no x values.

In the context of functions, what does the term 'range' refer to?

• The set of all x values.

• The set of all y values.

• The difference between the largest and smallest x values.

• The difference between the largest and smallest y values.

What should you do to verify if a table represents a function?

• Check if the table has more x values than y values.

• Check if each y value has multiple x values.

• Check if each x value has exactly one y value.

• Check if the table has more y values than x values.