Exploring Functions, Domain, and Range

This video tutorial covers the concepts of relations and functions, explaining how ordered pairs form relations and how mappings visually represent them. It defines functions as relations where each x-value maps to a single y-value and introduces one-to-one functions, where each y-value maps from a single x-value. The video also explains the vertical and horizontal line tests used to determine if a graph represents a function or a one-to-one function. Finally, it discusses domain and range, teaching how to determine these from graphs using interval notation.

What is a relation in mathematics?

• A set of unordered pairs

• A single point in XY form

• A function with multiple outputs

• A set of ordered pairs or points in XY form

In a mapping, what do the arrows represent?

• The distance between points

• The direction of the wind

• The relationship between X and Y values

• The size of the circles

What makes a relation a function?

• Every X value is mapped to exactly one Y value

• Every Y value is mapped to exactly one X value

• X values can map to multiple Y values

• Y values can map to multiple X values

Which of the following would make a relation not a function?

• All Y values map to the same X value

• All X values map to the same Y value

• One Y value maps to two different X values

• One X value maps to two different Y values

What is a one-to-one function?

• A function where every Y value is mapped from exactly one X value

• A function where every X value is mapped from exactly one Y value

• A relation where Y values can map to multiple X values

• A relation where X values can map to multiple Y values

What test must a graph pass to be considered a function?

• Vertical line test

• Curved line test

• Horizontal line test

• Diagonal line test

What additional test must a graph pass to be considered a one-to-one function?

• Diagonal line test

• Curved line test

• Horizontal line test

• Vertical line test

What is the domain of a relation?

• The set of all Y values

• The set of all points

• The set of all ordered pairs

• The set of all X values

What is the range of a relation?

• The set of all points

• The set of all ordered pairs

• The set of all Y values

• The set of all X values

In interval notation, what do brackets around numbers indicate?

• The interval is undefined

• The numbers are included in the interval

• The interval is infinite

• The numbers are excluded from the interval