Determining Domain and Range from Graphs

The video tutorial explains how to determine the domain and range of a function using its graph. It covers the concepts of domain and range, illustrating how to project a function onto the x-axis and y-axis to analyze its behavior. Two examples are provided to demonstrate how to identify the domain and range using interval notation and inequalities.

What is the domain of a function?

• The set of all possible z values

• The set of all possible y values

• The set of all possible x values

• The set of all possible w values

How do you determine the domain of a function from its graph?

• By analyzing the graph from top to bottom

• By analyzing the graph from right to left

• By projecting the function onto the y-axis

• By projecting the function onto the x-axis

What does an open point on the graph indicate about the domain?

• The value is included in the domain

• The value is the minimum of the domain

• The value is not included in the domain

• The value is the maximum of the domain

How is the domain expressed using interval notation if it includes 4 but not -2?

• [4, -2)

• [-2, 4]

• (-2, 4]

• (-2, 4)

What is the range of a function?

• The set of all possible x values

• The set of all possible y values

• The set of all possible z values

• The set of all possible w values

How do you determine the range of a function from its graph?

• By projecting the function onto the x-axis

• By analyzing the graph from left to right

• By projecting the function onto the y-axis

• By analyzing the graph from bottom to top

What does a closed point on the graph indicate about the range?

• The value is included in the range

• The value is not included in the range

• The value is the maximum of the range

• The value is the minimum of the range

In the second example, what is the domain of the function?

• From -2 to 2, not including both -2 and 2

• From -2 to 2, including -2 but not including 2

• From -2 to 2, not including -2 but including 2

• From -2 to 2, including both -2 and 2

In the second example, what is the range of the function?

• From -4 to 4, including both -4 and 4

• From -4 to 4, not including -4 but including 4

• From -4 to 4, including -4 but not including 4

• From -4 to 4, not including both -4 and 4

How is the range expressed using interval notation if it includes -4 but not 4?

• (-4, 4]

• [-4, 4]

• [4, -4)

• (-4, 4)