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, showing how to project the graph onto the x-axis to find the domain and onto the y-axis to find the range. The tutorial provides examples, illustrating how to express domain and range using inequalities and interval notation. It emphasizes the importance of open and closed points on the graph and how they affect the inclusion of values in the domain and range.

What is the domain of a function?

• All possible y-values of the function

• The lowest point on the graph

• The highest point on the graph

• All possible x-values of the function

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

• By projecting the graph onto the x-axis

• By finding the lowest point on the graph

• By projecting the graph onto the y-axis

• By finding the highest point on the graph

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

• The value is included in the domain

• The value is not included in the domain

• The value is the lowest point

• The value is the highest point

How would you express the domain of a function that includes all x-values from -3 to 2, excluding -3?

• x < -3 and x ≥ 2

• x ≤ -3 and x > 2

• x ≥ -3 and x < 2

• x > -3 and x ≤ 2

What is the range of a function?

• All possible y-values of the function

• All possible x-values of the function

• The lowest point on the graph

• The highest point on the graph

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

• By projecting the graph onto the y-axis

• By finding the highest point on the graph

• By projecting the graph onto the x-axis

• By finding the lowest point on the graph

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

• The value is the lowest point

• The value is the highest point

• The value is not included in the range

• The value is included in the range

How would you express the range of a function that includes all y-values from -5 to 5, excluding -5?

• y ≤ -5 and y > 5

• y < -5 and y ≥ 5

• y ≥ -5 and y < 5

• y > -5 and y ≤ 5

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

• x > -4

• x ≥ -4

• x ≤ -4

• x < -4

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

• y > -4

• y ≥ -4

• y ≤ -4

• y < -4