Exploring Functions in 8.5G

The video tutorial introduces the concept of functions, explaining how to identify them using ordered pairs, tables, mappings, and graphs. It emphasizes the rule that each input (X) must have a unique output (Y) and demonstrates this through examples. The tutorial also covers the vertical line test for graphically determining functions, highlighting that no X values should repeat for a relation to be a function.

What is essential for a set of ordered pairs to be considered a function?

• Both x and y values must be positive.

• Each x value must be unique.

• The ordered pairs must form a straight line.

• Each y value must be unique.

How can you tell if a set of ordered pairs does not represent a function?

• If the y values are not in ascending order

• If it forms a straight line on a graph

• If any x value appears more than once

• If it includes both positive and negative numbers

What does each input having only one output imply in a function?

• There can be multiple x values for one y value.

• There can be multiple y values for one x value.

• Each x value corresponds to exactly one y value.

• Each y value corresponds to exactly one x value.

What is a linear function?

• A function where the graph is a straight line

• A function with only positive x values

• A function where each x value has multiple y values

• A function that includes only whole numbers

In a table representing a function, what is not allowed?

• Repeated y values

• Decimal numbers

• Negative numbers

• Repeated x values

What is true about the y values in a function?

• They cannot be zero

• They must be in ascending order

• They can repeat

• They must all be unique

What indicates a mapping is not a function?

• If the mapping includes negative numbers

• If all lines are straight

• If there is more than one line coming from an x

• If there is exactly one line coming from each x

What is the vertical line test used for?

• To determine if a graph represents a linear function

• To find the slope of a graph

• To measure the distance between points on a graph

• To check if a graph represents a function

What does it mean if a graph passes the vertical line test?

• It represents a function

• All its values are positive

• It has repeated x values

• It does not represent a function

In the context of functions, what is the significance of 'no repeated x's'?

• It means the function cannot have negative values

• It is necessary for the function to have a graph

• It ensures the function is linear

• It is a rule to determine if a relationship is a function