Understanding Domain and Range

The video tutorial explains the concepts of domain and range in the context of functions. It begins by defining a function and its domain and range. The tutorial then examines two functions, identifying the domain and range for each. The first function has a limited domain and range due to open circles on the graph, while the second function has a domain and range that include all real numbers.

What is the domain of a function?

• The set of all negative numbers

• The set of all positive numbers

• The set of all possible inputs

• The set of all possible outputs

Why is the function not defined at x = 8 for the first function?

• Because x = 8 is not a real number

• Because there is an open circle at x = 8

• Because there is a closed circle at x = 8

• Because x = 8 is outside the graph

What does an open circle on a graph indicate?

• The value is included

• The value is not included

• The value is zero

• The value is negative

What does a closed circle on a graph indicate?

• The value is zero

• The value is negative

• The value is not included

• The value is included

What is the smallest value in the domain of the first function?

• 0

• -6

• -4

• 4

What is the range of the first function?

• All values from 2 to 8, excluding 2

• All values from 2 to 8, including both

• All values from 2 to 8, excluding both

• All values from 2 to 8, excluding 8

What is the highest value the first function can take?

• 8

• 6

• 4

• 2

What is the domain of the second function?

• All real numbers

• All positive numbers

• All negative numbers

• All integers

What is the range of the second function?

• All positive numbers

• All real numbers

• All negative numbers

• All integers

Why can the range of the second function be considered all real numbers?

• Because the graph is a vertical line

• Because the graph is a parabola

• Because the graph is a horizontal line

• Because the graph extends infinitely in both directions