Exploring Domain and Range with Set-Builder and Interval Notation

The video tutorial covers the concepts of domain and range in mathematics, focusing on how to write and interpret them using set builder and interval notation. It explains the domain as the set of all possible x-values and the range as the set of all possible y-values. The tutorial also analyzes a complex function, highlighting the importance of open and closed circles in determining domain and range. Additionally, it demonstrates how to use tables and maps to understand these concepts better.

What does the domain of a function represent?

• The set of all possible y-values

• The highest point on the graph

• The lowest point on the graph

• The set of all possible x-values

In set builder notation, what does the symbol '∈' represent?

• Such that

• Is an element of

• Is greater than

• Is less than

How is the domain of a function that extends infinitely to the left and right represented in interval notation?

• [0, ∞)

• (-∞, ∞)

• [0, 1]

• (-∞, 0]

What does a 'soft bracket' in interval notation indicate?

• The value is zero

• The value is not included

• The value is infinity

• The value is included

What is the range of a function that starts at -3 and goes up to infinity?

• (-∞, -3]

• [-3, ∞)

• (-3, ∞)

• [0, ∞)

In set builder notation, how would you represent all y-values greater than or equal to -3?

• {y | y ≤ -3}

• {y | y ≥ -3}

• {x | x ≤ -3}

• {x | x ≥ -3}

What does the 'U' symbol represent in interval notation?

• Superset

• Subset

• Union

• Intersection

How is an open circle on a graph represented in interval notation?

• With a curly brace

• With a parenthesis

• With a soft bracket

• With a hard bracket

In a table, if an x-value is repeated, how many times should it be listed in the domain?

• Once

• Twice

• Three times

• As many times as it appears

What is the domain of the function if the x-values are 1, 2, 3, and 4?

• {0, 1, 2, 3}

• {-∞, ∞}

• {1, 2, 3, 4}

• {-4, -3, 4, 6}