Understanding Domain and Range

The video tutorial explains how to determine the domain and range of functions using interval notation. It covers the analysis of the cubic function y = x^3 + 2, showing that both its domain and range are all real numbers. The quadratic function y = x^2 - 3 is also analyzed, with its domain being all real numbers and its range starting from -3 to infinity. The tutorial emphasizes understanding these concepts through graph analysis.

What is the domain of a function?

• The set of all positive values

• The set of all possible output values

• The set of all possible input values

• The set of all negative values

For the function y = x^3 + 2, what is the domain?

• All negative numbers

• Only integers

• All real numbers

• All positive numbers

How is the domain of y = x^3 + 2 expressed in interval notation?

• (-∞, ∞)

• (-∞, 0]

• [0, 1]

• [0, ∞)

What is the range of the function y = x^3 + 2?

• Only negative numbers

• All real numbers

• Only integers

• Only positive numbers

In interval notation, how is the range of y = x^3 + 2 represented?

• [0, ∞)

• (-∞, ∞)

• (-∞, 0]

• [1, ∞)

What is the domain of the function y = x^2 - 3?

• Only integers

• Only negative numbers

• Only positive numbers

• All real numbers

How is the domain of y = x^2 - 3 expressed in interval notation?

• (-∞, ∞)

• [0, ∞)

• [1, ∞)

• (-∞, 0]

What is the lowest point on the graph of y = x^2 - 3?

• y = 0

• y = 3

• y = -1

• y = -3

In interval notation, how is the range of y = x^2 - 3 represented?

• (-∞, ∞)

• (-3, ∞)

• [0, ∞)

• [-3, ∞)

What does a square bracket in interval notation indicate?

• The interval is undefined

• The interval is open

• The interval is infinite

• The interval is closed