Exploring Domain, Range, and Functions in Ordered Pairs

The video tutorial explains how to find the domain and range of a relation given as a set of ordered pairs. It describes the domain as the set of all possible inputs and the range as the set of all possible outputs. The tutorial then explores how to determine if a relation is a function by ensuring each input has exactly one output, using a mapping method. It also introduces the vertical line test as a graphical method to verify if a relation is a function, emphasizing that a vertical line should not intersect the graph more than once.

What does each ordered pair in a relation represent?

• A set of outputs

• A set of inputs

• An input and its corresponding output

• A function

What is the domain of the relation given the ordered pairs (5, -7), (4, -7), (3, -7), (2, -7)?

• {2, 3, 4, 5}

• {5, 4, 3, 2}

• {-7}

• {-7, 2, 3, 4, 5}

How should the values in the domain be listed?

• Alphabetically

• From least to greatest

• From greatest to least

• In any order

What is the range of the relation given the ordered pairs (5, -7), (4, -7), (3, -7), (2, -7)?

• {-7}

• {2, 3, 4, 5}

• {5, 4, 3, 2}

• {-7, 2, 3, 4, 5}

What defines a function in terms of input and output?

• Each output has multiple inputs

• Each output has exactly one input

• Each input has exactly one output

• Each input has multiple outputs

In a mapping diagram, what does an arrow from an input to an output represent?

• The input is less than the output

• The input is equal to the output

• The input is greater than the output

• The input corresponds to the output

What would indicate that a relation is not a function in a mapping diagram?

• An output has multiple inputs

• An output has no input

• An input has multiple outputs

• An input has no output

What does the vertical line test determine?

• If a graph is linear

• If a graph is quadratic

• If a relation is a function

• If a relation is one-to-one

What happens if a vertical line intersects a graph of a relation more than once?

• The graph is linear

• The relation is not a function

• The graph is quadratic

• The relation is a function

What can be concluded if a vertical line intersects a graph at most once?

• The relation is a function

• The relation is not a function

• The graph is linear

• The graph is quadratic