Exploring Domain and Range from Graphs

This video tutorial reviews the concepts of domain and range in graphs, focusing on how to identify them using examples. It explains the use of compound inequalities to represent domains and ranges, and discusses special cases such as infinite domains and ranges, and graphs with open or closed circles. The tutorial aims to clarify these concepts for students, providing practical tips and examples to aid understanding.

What is the domain of a function?

• The lowest point on the graph

• The highest point on the graph

• All possible x-values

• All possible y-values

How should you represent the domain of a function using inequalities?

• As a set of separate inequalities

• As a compound inequality

• As a single inequality

• As a list of points

What does the compound inequality -3 ≤ x ≤ 3 represent?

• x is between -3 and 3, inclusive

• x is exactly -3 or 3

• x is greater than -3 and less than 3

• x is less than -3 or greater than 3

What is the range of a function?

• The lowest point on the graph

• The highest point on the graph

• All possible y-values

• All possible x-values

How should you represent the range of a function using inequalities?

• As a single inequality

• As a compound inequality

• As a list of points

• As a set of separate inequalities

If a graph has arrows indicating it continues indefinitely, what is the domain?

• All positive numbers

• All integers

• All negative numbers

• All real numbers

For a graph with arrows, what is the range if it continues upwards indefinitely but stops at y = -3?

• y ≥ -3

• y > -3

• y ≤ -3

• y = -3

What does an open circle on a graph indicate about that point?

• The point is the minimum value

• The point is not included

• The point is included

• The point is the maximum value

How would you write the domain for a graph that starts at x = -5 and ends at x = 4, with an open circle at x = -5?

• -5 ≤ x ≤ 4

• -5 < x < 4

• -5 < x ≤ 4

• -5 ≤ x < 4

How would you write the range for a graph that starts at y = -2 and ends at y = 3, with an open circle at y = -2?

• -2 < y < 3

• -2 ≤ y ≤ 3

• -2 < y ≤ 3

• -2 ≤ y < 3