Understanding 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, how to project a graph onto the x-axis to find the domain, and onto the y-axis to find the range. The tutorial provides examples, showing how to express domain and range using inequalities and interval notation, and highlights the importance of open and closed points on the graph.

What is the domain of a function?

• The set of all possible x-values of the function.

• The set of all possible values of the function.

• The set of all possible y-values of the function.

• The set of all possible z-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 projecting the graph onto the z-axis.

• By projecting the graph onto the y-axis.

• By projecting the graph onto the w-axis.

In interval notation, how is an open point represented?

• With a straight line.

• With a square bracket.

• With a curly bracket.

• With a rounded parenthesis.

What is the range of a function?

• The set of all possible x-values of the function.

• The set of all possible y-values of the function.

• The set of all possible z-values of the function.

• The set of all possible values of the function.

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

• By projecting the graph onto the w-axis.

• By projecting the graph onto the z-axis.

• By projecting the graph onto the y-axis.

• By projecting the graph onto the x-axis.

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

• x is less than or equal to negative four.

• x is less than or equal to positive four.

• x is greater than or equal to negative four.

• x is greater than or equal to positive four.

In the second example, how is the domain expressed in interval notation?

• From negative four to positive four.

• From negative four to infinity.

• From zero to infinity.

• From zero to negative four.

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

• y is greater than or equal to positive four.

• y is less than or equal to positive four.

• y is greater than or equal to negative four.

• y is less than or equal to negative four.

In the second example, how is the range expressed in interval notation?

• From negative four to infinity.

• From zero to infinity.

• From zero to negative four.

• From negative four to positive four.

What does a closed point on a graph indicate?

• The value is not included in the domain or range.

• The value is optional in the domain or range.

• The value is excluded from the domain or range.

• The value is included in the domain or range.